All Answers 355923 Answers

Believe it or not, there is actually a formula for that and it goes like this:

nCr =[Number of elements + Combination size - 1]C5 =[9+5-1]C5 =13C5 =1,287 combinations with desired repeats. If you don't believe me, I had my computer list them all, and here they are!!:

{1, 1, 1, 1, 1}, {1, 1, 1, 1, 2}, {1, 1, 1, 1, 3}, {1, 1, 1, 1, 4}, {1, 1, 1, 1, 5}, {1, 1, 1, 1, 6}, {1, 1, 1, 1, 7}, {1, 1, 1, 1, 8}, {1, 1, 1, 1, 9}, {1, 1, 1, 2, 2}, {1, 1, 1, 2, 3}, {1, 1, 1, 2, 4}, {1, 1, 1, 2, 5}, {1, 1, 1, 2, 6}, {1, 1, 1, 2, 7}, {1, 1, 1, 2, 8}, {1, 1, 1, 2, 9}, {1, 1, 1, 3, 3}, {1, 1, 1, 3, 4}, {1, 1, 1, 3, 5}, {1, 1, 1, 3, 6}, {1, 1, 1, 3, 7}, {1, 1, 1, 3, 8}, {1, 1, 1, 3, 9}, {1, 1, 1, 4, 4}, {1, 1, 1, 4, 5}, {1, 1, 1, 4, 6}, {1, 1, 1, 4, 7}, {1, 1, 1, 4, 8}, {1, 1, 1, 4, 9}, {1, 1, 1, 5, 5}, {1, 1, 1, 5, 6}, {1, 1, 1, 5, 7}, {1, 1, 1, 5, 8}, {1, 1, 1, 5, 9}, {1, 1, 1, 6, 6}, {1, 1, 1, 6, 7}, {1, 1, 1, 6, 8}, {1, 1, 1, 6, 9}, {1, 1, 1, 7, 7}, {1, 1, 1, 7, 8}, {1, 1, 1, 7, 9}, {1, 1, 1, 8, 8}, {1, 1, 1, 8, 9}, {1, 1, 1, 9, 9}, {1, 1, 2, 2, 2}, {1, 1, 2, 2, 3}, {1, 1, 2, 2, 4}, {1, 1, 2, 2, 5}, {1, 1, 2, 2, 6}, {1, 1, 2, 2, 7}, {1, 1, 2, 2, 8}, {1, 1, 2, 2, 9}, {1, 1, 2, 3, 3}, {1, 1, 2, 3, 4}, {1, 1, 2, 3, 5}, {1, 1, 2, 3, 6}, {1, 1, 2, 3, 7}, {1, 1, 2, 3, 8}, {1, 1, 2, 3, 9}, {1, 1, 2, 4, 4}, {1, 1, 2, 4, 5}, {1, 1, 2, 4, 6}, {1, 1, 2, 4, 7}, {1, 1, 2, 4, 8}, {1, 1, 2, 4, 9}, {1, 1, 2, 5, 5}, {1, 1, 2, 5, 6}, {1, 1, 2, 5, 7}, {1, 1, 2, 5, 8}, {1, 1, 2, 5, 9}, {1, 1, 2, 6, 6}, {1, 1, 2, 6, 7}, {1, 1, 2, 6, 8}, {1, 1, 2, 6, 9}, {1, 1, 2, 7, 7}, {1, 1, 2, 7, 8}, {1, 1, 2, 7, 9}, {1, 1, 2, 8, 8}, {1, 1, 2, 8, 9}, {1, 1, 2, 9, 9}, {1, 1, 3, 3, 3}, {1, 1, 3, 3, 4}, {1, 1, 3, 3, 5}, {1, 1, 3, 3, 6}, {1, 1, 3, 3, 7}, {1, 1, 3, 3, 8}, {1, 1, 3, 3, 9}, {1, 1, 3, 4, 4}, {1, 1, 3, 4, 5}, {1, 1, 3, 4, 6}, {1, 1, 3, 4, 7}, {1, 1, 3, 4, 8}, {1, 1, 3, 4, 9}, {1, 1, 3, 5, 5}, {1, 1, 3, 5, 6}, {1, 1, 3, 5, 7}, {1, 1, 3, 5, 8}, {1, 1, 3, 5, 9}, {1, 1, 3, 6, 6}, {1, 1, 3, 6, 7}, {1, 1, 3, 6, 8}, {1, 1, 3, 6, 9}, {1, 1, 3, 7, 7}, {1, 1, 3, 7, 8}, {1, 1, 3, 7, 9}, {1, 1, 3, 8, 8}, {1, 1, 3, 8, 9}, {1, 1, 3, 9, 9}, {1, 1, 4, 4, 4}, {1, 1, 4, 4, 5}, {1, 1, 4, 4, 6}, {1, 1, 4, 4, 7}, {1, 1, 4, 4, 8}, {1, 1, 4, 4, 9}, {1, 1, 4, 5, 5}, {1, 1, 4, 5, 6}, {1, 1, 4, 5, 7}, {1, 1, 4, 5, 8}, {1, 1, 4, 5, 9}, {1, 1, 4, 6, 6}, {1, 1, 4, 6, 7}, {1, 1, 4, 6, 8}, {1, 1, 4, 6, 9}, {1, 1, 4, 7, 7}, {1, 1, 4, 7, 8}, {1, 1, 4, 7, 9}, {1, 1, 4, 8, 8}, {1, 1, 4, 8, 9}, {1, 1, 4, 9, 9}, {1, 1, 5, 5, 5}, {1, 1, 5, 5, 6}, {1, 1, 5, 5, 7}, {1, 1, 5, 5, 8}, {1, 1, 5, 5, 9}, {1, 1, 5, 6, 6}, {1, 1, 5, 6, 7}, {1, 1, 5, 6, 8}, {1, 1, 5, 6, 9}, {1, 1, 5, 7, 7}, {1, 1, 5, 7, 8}, {1, 1, 5, 7, 9}, {1, 1, 5, 8, 8}, {1, 1, 5, 8, 9}, {1, 1, 5, 9, 9}, {1, 1, 6, 6, 6}, {1, 1, 6, 6, 7}, {1, 1, 6, 6, 8}, {1, 1, 6, 6, 9}, {1, 1, 6, 7, 7}, {1, 1, 6, 7, 8}, {1, 1, 6, 7, 9}, {1, 1, 6, 8, 8}, {1, 1, 6, 8, 9}, {1, 1, 6, 9, 9}, {1, 1, 7, 7, 7}, {1, 1, 7, 7, 8}, {1, 1, 7, 7, 9}, {1, 1, 7, 8, 8}, {1, 1, 7, 8, 9}, {1, 1, 7, 9, 9}, {1, 1, 8, 8, 8}, {1, 1, 8, 8, 9}, {1, 1, 8, 9, 9}, {1, 1, 9, 9, 9}, {1, 2, 2, 2, 2}, {1, 2, 2, 2, 3}, {1, 2, 2, 2, 4}, {1, 2, 2, 2, 5}, {1, 2, 2, 2, 6}, {1, 2, 2, 2, 7}, {1, 2, 2, 2, 8}, {1, 2, 2, 2, 9}, {1, 2, 2, 3, 3}, {1, 2, 2, 3, 4}, {1, 2, 2, 3, 5}, {1, 2, 2, 3, 6}, {1, 2, 2, 3, 7}, {1, 2, 2, 3, 8}, {1, 2, 2, 3, 9}, {1, 2, 2, 4, 4}, {1, 2, 2, 4, 5}, {1, 2, 2, 4, 6}, {1, 2, 2, 4, 7}, {1, 2, 2, 4, 8}, {1, 2, 2, 4, 9}, {1, 2, 2, 5, 5}, {1, 2, 2, 5, 6}, {1, 2, 2, 5, 7}, {1, 2, 2, 5, 8}, {1, 2, 2, 5, 9}, {1, 2, 2, 6, 6}, {1, 2, 2, 6, 7}, {1, 2, 2, 6, 8}, {1, 2, 2, 6, 9}, {1, 2, 2, 7, 7}, {1, 2, 2, 7, 8}, {1, 2, 2, 7, 9}, {1, 2, 2, 8, 8}, {1, 2, 2, 8, 9}, {1, 2, 2, 9, 9}, {1, 2, 3, 3, 3}, {1, 2, 3, 3, 4}, {1, 2, 3, 3, 5}, {1, 2, 3, 3, 6}, {1, 2, 3, 3, 7}, {1, 2, 3, 3, 8}, {1, 2, 3, 3, 9}, {1, 2, 3, 4, 4}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 4, 7}, {1, 2, 3, 4, 8}, {1, 2, 3, 4, 9}, {1, 2, 3, 5, 5}, {1, 2, 3, 5, 6}, {1, 2, 3, 5, 7}, {1, 2, 3, 5, 8}, {1, 2, 3, 5, 9}, {1, 2, 3, 6, 6}, {1, 2, 3, 6, 7}, {1, 2, 3, 6, 8}, {1, 2, 3, 6, 9}, {1, 2, 3, 7, 7}, {1, 2, 3, 7, 8}, {1, 2, 3, 7, 9}, {1, 2, 3, 8, 8}, {1, 2, 3, 8, 9}, {1, 2, 3, 9, 9}, {1, 2, 4, 4, 4}, {1, 2, 4, 4, 5}, {1, 2, 4, 4, 6}, {1, 2, 4, 4, 7}, {1, 2, 4, 4, 8}, {1, 2, 4, 4, 9}, {1, 2, 4, 5, 5}, {1, 2, 4, 5, 6}, {1, 2, 4, 5, 7}, {1, 2, 4, 5, 8}, {1, 2, 4, 5, 9}, {1, 2, 4, 6, 6}, {1, 2, 4, 6, 7}, {1, 2, 4, 6, 8}, {1, 2, 4, 6, 9}, {1, 2, 4, 7, 7}, {1, 2, 4, 7, 8}, {1, 2, 4, 7, 9}, {1, 2, 4, 8, 8}, {1, 2, 4, 8, 9}, {1, 2, 4, 9, 9}, {1, 2, 5, 5, 5}, {1, 2, 5, 5, 6}, {1, 2, 5, 5, 7}, {1, 2, 5, 5, 8}, {1, 2, 5, 5, 9}, {1, 2, 5, 6, 6}, {1, 2, 5, 6, 7}, {1, 2, 5, 6, 8}, {1, 2, 5, 6, 9}, {1, 2, 5, 7, 7}, {1, 2, 5, 7, 8}, {1, 2, 5, 7, 9}, {1, 2, 5, 8, 8}, {1, 2, 5, 8, 9}, {1, 2, 5, 9, 9}, {1, 2, 6, 6, 6}, {1, 2, 6, 6, 7}, {1, 2, 6, 6, 8}, {1, 2, 6, 6, 9}, {1, 2, 6, 7, 7}, {1, 2, 6, 7, 8}, {1, 2, 6, 7, 9}, {1, 2, 6, 8, 8}, {1, 2, 6, 8, 9}, {1, 2, 6, 9, 9}, {1, 2, 7, 7, 7}, {1, 2, 7, 7, 8}, {1, 2, 7, 7, 9}, {1, 2, 7, 8, 8}, {1, 2, 7, 8, 9}, {1, 2, 7, 9, 9}, {1, 2, 8, 8, 8}, {1, 2, 8, 8, 9}, {1, 2, 8, 9, 9}, {1, 2, 9, 9, 9}, {1, 3, 3, 3, 3}, {1, 3, 3, 3, 4}, {1, 3, 3, 3, 5}, {1, 3, 3, 3, 6}, {1, 3, 3, 3, 7}, {1, 3, 3, 3, 8}, {1, 3, 3, 3, 9}, {1, 3, 3, 4, 4}, {1, 3, 3, 4, 5}, {1, 3, 3, 4, 6}, {1, 3, 3, 4, 7}, {1, 3, 3, 4, 8}, {1, 3, 3, 4, 9}, {1, 3, 3, 5, 5}, {1, 3, 3, 5, 6}, {1, 3, 3, 5, 7}, {1, 3, 3, 5, 8}, {1, 3, 3, 5, 9}, {1, 3, 3, 6, 6}, {1, 3, 3, 6, 7}, {1, 3, 3, 6, 8}, {1, 3, 3, 6, 9}, {1, 3, 3, 7, 7}, {1, 3, 3, 7, 8}, {1, 3, 3, 7, 9}, {1, 3, 3, 8, 8}, {1, 3, 3, 8, 9}, {1, 3, 3, 9, 9}, {1, 3, 4, 4, 4}, {1, 3, 4, 4, 5}, {1, 3, 4, 4, 6}, {1, 3, 4, 4, 7}, {1, 3, 4, 4, 8}, {1, 3, 4, 4, 9}, {1, 3, 4, 5, 5}, {1, 3, 4, 5, 6}, {1, 3, 4, 5, 7}, {1, 3, 4, 5, 8}, {1, 3, 4, 5, 9}, {1, 3, 4, 6, 6}, {1, 3, 4, 6, 7}, {1, 3, 4, 6, 8}, {1, 3, 4, 6, 9}, {1, 3, 4, 7, 7}, {1, 3, 4, 7, 8}, {1, 3, 4, 7, 9}, {1, 3, 4, 8, 8}, {1, 3, 4, 8, 9}, {1, 3, 4, 9, 9}, {1, 3, 5, 5, 5}, {1, 3, 5, 5, 6}, {1, 3, 5, 5, 7}, {1, 3, 5, 5, 8}, {1, 3, 5, 5, 9}, {1, 3, 5, 6, 6}, {1, 3, 5, 6, 7}, {1, 3, 5, 6, 8}, {1, 3, 5, 6, 9}, {1, 3, 5, 7, 7}, {1, 3, 5, 7, 8}, {1, 3, 5, 7, 9}, {1, 3, 5, 8, 8}, {1, 3, 5, 8, 9}, {1, 3, 5, 9, 9}, {1, 3, 6, 6, 6}, {1, 3, 6, 6, 7}, {1, 3, 6, 6, 8}, {1, 3, 6, 6, 9}, {1, 3, 6, 7, 7}, {1, 3, 6, 7, 8}, {1, 3, 6, 7, 9}, {1, 3, 6, 8, 8}, {1, 3, 6, 8, 9}, {1, 3, 6, 9, 9}, {1, 3, 7, 7, 7}, {1, 3, 7, 7, 8}, {1, 3, 7, 7, 9}, {1, 3, 7, 8, 8}, {1, 3, 7, 8, 9}, {1, 3, 7, 9, 9}, {1, 3, 8, 8, 8}, {1, 3, 8, 8, 9}, {1, 3, 8, 9, 9}, {1, 3, 9, 9, 9}, {1, 4, 4, 4, 4}, {1, 4, 4, 4, 5}, {1, 4, 4, 4, 6}, {1, 4, 4, 4, 7}, {1, 4, 4, 4, 8}, {1, 4, 4, 4, 9}, {1, 4, 4, 5, 5}, {1, 4, 4, 5, 6}, {1, 4, 4, 5, 7}, {1, 4, 4, 5, 8}, {1, 4, 4, 5, 9}, {1, 4, 4, 6, 6}, {1, 4, 4, 6, 7}, {1, 4, 4, 6, 8}, {1, 4, 4, 6, 9}, {1, 4, 4, 7, 7}, {1, 4, 4, 7, 8}, {1, 4, 4, 7, 9}, {1, 4, 4, 8, 8}, {1, 4, 4, 8, 9}, {1, 4, 4, 9, 9}, {1, 4, 5, 5, 5}, {1, 4, 5, 5, 6}, {1, 4, 5, 5, 7}, {1, 4, 5, 5, 8}, {1, 4, 5, 5, 9}, {1, 4, 5, 6, 6}, {1, 4, 5, 6, 7}, {1, 4, 5, 6, 8}, {1, 4, 5, 6, 9}, {1, 4, 5, 7, 7}, {1, 4, 5, 7, 8}, {1, 4, 5, 7, 9}, {1, 4, 5, 8, 8}, {1, 4, 5, 8, 9}, {1, 4, 5, 9, 9}, {1, 4, 6, 6, 6}, {1, 4, 6, 6, 7}, {1, 4, 6, 6, 8}, {1, 4, 6, 6, 9}, {1, 4, 6, 7, 7}, {1, 4, 6, 7, 8}, {1, 4, 6, 7, 9}, {1, 4, 6, 8, 8}, {1, 4, 6, 8, 9}, {1, 4, 6, 9, 9}, {1, 4, 7, 7, 7}, {1, 4, 7, 7, 8}, {1, 4, 7, 7, 9}, {1, 4, 7, 8, 8}, {1, 4, 7, 8, 9}, {1, 4, 7, 9, 9}, {1, 4, 8, 8, 8}, {1, 4, 8, 8, 9}, {1, 4, 8, 9, 9}, {1, 4, 9, 9, 9}, {1, 5, 5, 5, 5}, {1, 5, 5, 5, 6}, {1, 5, 5, 5, 7}, {1, 5, 5, 5, 8}, {1, 5, 5, 5, 9}, {1, 5, 5, 6, 6}, {1, 5, 5, 6, 7}, {1, 5, 5, 6, 8}, {1, 5, 5, 6, 9}, {1, 5, 5, 7, 7}, {1, 5, 5, 7, 8}, {1, 5, 5, 7, 9}, {1, 5, 5, 8, 8}, {1, 5, 5, 8, 9}, {1, 5, 5, 9, 9}, {1, 5, 6, 6, 6}, {1, 5, 6, 6, 7}, {1, 5, 6, 6, 8}, {1, 5, 6, 6, 9}, {1, 5, 6, 7, 7}, {1, 5, 6, 7, 8}, {1, 5, 6, 7, 9}, {1, 5, 6, 8, 8}, {1, 5, 6, 8, 9}, {1, 5, 6, 9, 9}, {1, 5, 7, 7, 7}, {1, 5, 7, 7, 8}, {1, 5, 7, 7, 9}, {1, 5, 7, 8, 8}, {1, 5, 7, 8, 9}, {1, 5, 7, 9, 9}, {1, 5, 8, 8, 8}, {1, 5, 8, 8, 9}, {1, 5, 8, 9, 9}, {1, 5, 9, 9, 9}, {1, 6, 6, 6, 6}, {1, 6, 6, 6, 7}, {1, 6, 6, 6, 8}, {1, 6, 6, 6, 9}, {1, 6, 6, 7, 7}, {1, 6, 6, 7, 8}, {1, 6, 6, 7, 9}, {1, 6, 6, 8, 8}, {1, 6, 6, 8, 9}, {1, 6, 6, 9, 9}, {1, 6, 7, 7, 7}, {1, 6, 7, 7, 8}, {1, 6, 7, 7, 9}, {1, 6, 7, 8, 8}, {1, 6, 7, 8, 9}, {1, 6, 7, 9, 9}, {1, 6, 8, 8, 8}, {1, 6, 8, 8, 9}, {1, 6, 8, 9, 9}, {1, 6, 9, 9, 9}, {1, 7, 7, 7, 7}, {1, 7, 7, 7, 8}, {1, 7, 7, 7, 9}, {1, 7, 7, 8, 8}, {1, 7, 7, 8, 9}, {1, 7, 7, 9, 9}, {1, 7, 8, 8, 8}, {1, 7, 8, 8, 9}, {1, 7, 8, 9, 9}, {1, 7, 9, 9, 9}, {1, 8, 8, 8, 8}, {1, 8, 8, 8, 9}, {1, 8, 8, 9, 9}, {1, 8, 9, 9, 9}, {1, 9, 9, 9, 9}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 3}, {2, 2, 2, 2, 4}, {2, 2, 2, 2, 5}, {2, 2, 2, 2, 6}, {2, 2, 2, 2, 7}, {2, 2, 2, 2, 8}, {2, 2, 2, 2, 9}, {2, 2, 2, 3, 3}, {2, 2, 2, 3, 4}, {2, 2, 2, 3, 5}, {2, 2, 2, 3, 6}, {2, 2, 2, 3, 7}, {2, 2, 2, 3, 8}, {2, 2, 2, 3, 9}, {2, 2, 2, 4, 4}, {2, 2, 2, 4, 5}, {2, 2, 2, 4, 6}, {2, 2, 2, 4, 7}, {2, 2, 2, 4, 8}, {2, 2, 2, 4, 9}, {2, 2, 2, 5, 5}, {2, 2, 2, 5, 6}, {2, 2, 2, 5, 7}, {2, 2, 2, 5, 8}, {2, 2, 2, 5, 9}, {2, 2, 2, 6, 6}, {2, 2, 2, 6, 7}, {2, 2, 2, 6, 8}, {2, 2, 2, 6, 9}, {2, 2, 2, 7, 7}, {2, 2, 2, 7, 8}, {2, 2, 2, 7, 9}, {2, 2, 2, 8, 8}, {2, 2, 2, 8, 9}, {2, 2, 2, 9, 9}, {2, 2, 3, 3, 3}, {2, 2, 3, 3, 4}, {2, 2, 3, 3, 5}, {2, 2, 3, 3, 6}, {2, 2, 3, 3, 7}, {2, 2, 3, 3, 8}, {2, 2, 3, 3, 9}, {2, 2, 3, 4, 4}, {2, 2, 3, 4, 5}, {2, 2, 3, 4, 6}, {2, 2, 3, 4, 7}, {2, 2, 3, 4, 8}, {2, 2, 3, 4, 9}, {2, 2, 3, 5, 5}, {2, 2, 3, 5, 6}, {2, 2, 3, 5, 7}, {2, 2, 3, 5, 8}, {2, 2, 3, 5, 9}, {2, 2, 3, 6, 6}, {2, 2, 3, 6, 7}, {2, 2, 3, 6, 8}, {2, 2, 3, 6, 9}, {2, 2, 3, 7, 7}, {2, 2, 3, 7, 8}, {2, 2, 3, 7, 9}, {2, 2, 3, 8, 8}, {2, 2, 3, 8, 9}, {2, 2, 3, 9, 9}, {2, 2, 4, 4, 4}, {2, 2, 4, 4, 5}, {2, 2, 4, 4, 6}, {2, 2, 4, 4, 7}, {2, 2, 4, 4, 8}, {2, 2, 4, 4, 9}, {2, 2, 4, 5, 5}, {2, 2, 4, 5, 6}, {2, 2, 4, 5, 7}, {2, 2, 4, 5, 8}, {2, 2, 4, 5, 9}, {2, 2, 4, 6, 6}, {2, 2, 4, 6, 7}, {2, 2, 4, 6, 8}, {2, 2, 4, 6, 9}, {2, 2, 4, 7, 7}, {2, 2, 4, 7, 8}, {2, 2, 4, 7, 9}, {2, 2, 4, 8, 8}, {2, 2, 4, 8, 9}, {2, 2, 4, 9, 9}, {2, 2, 5, 5, 5}, {2, 2, 5, 5, 6}, {2, 2, 5, 5, 7}, {2, 2, 5, 5, 8}, {2, 2, 5, 5, 9}, {2, 2, 5, 6, 6}, {2, 2, 5, 6, 7}, {2, 2, 5, 6, 8}, {2, 2, 5, 6, 9}, {2, 2, 5, 7, 7}, {2, 2, 5, 7, 8}, {2, 2, 5, 7, 9}, {2, 2, 5, 8, 8}, {2, 2, 5, 8, 9}, {2, 2, 5, 9, 9}, {2, 2, 6, 6, 6}, {2, 2, 6, 6, 7}, {2, 2, 6, 6, 8}, {2, 2, 6, 6, 9}, {2, 2, 6, 7, 7}, {2, 2, 6, 7, 8}, {2, 2, 6, 7, 9}, {2, 2, 6, 8, 8}, {2, 2, 6, 8, 9}, {2, 2, 6, 9, 9}, {2, 2, 7, 7, 7}, {2, 2, 7, 7, 8}, {2, 2, 7, 7, 9}, {2, 2, 7, 8, 8}, {2, 2, 7, 8, 9}, {2, 2, 7, 9, 9}, {2, 2, 8, 8, 8}, {2, 2, 8, 8, 9}, {2, 2, 8, 9, 9}, {2, 2, 9, 9, 9}, {2, 3, 3, 3, 3}, {2, 3, 3, 3, 4}, {2, 3, 3, 3, 5}, {2, 3, 3, 3, 6}, {2, 3, 3, 3, 7}, {2, 3, 3, 3, 8}, {2, 3, 3, 3, 9}, {2, 3, 3, 4, 4}, {2, 3, 3, 4, 5}, {2, 3, 3, 4, 6}, {2, 3, 3, 4, 7}, {2, 3, 3, 4, 8}, {2, 3, 3, 4, 9}, {2, 3, 3, 5, 5}, {2, 3, 3, 5, 6}, {2, 3, 3, 5, 7}, {2, 3, 3, 5, 8}, {2, 3, 3, 5, 9}, {2, 3, 3, 6, 6}, {2, 3, 3, 6, 7}, {2, 3, 3, 6, 8}, {2, 3, 3, 6, 9}, {2, 3, 3, 7, 7}, {2, 3, 3, 7, 8}, {2, 3, 3, 7, 9}, {2, 3, 3, 8, 8}, {2, 3, 3, 8, 9}, {2, 3, 3, 9, 9}, {2, 3, 4, 4, 4}, {2, 3, 4, 4, 5}, {2, 3, 4, 4, 6}, {2, 3, 4, 4, 7}, {2, 3, 4, 4, 8}, {2, 3, 4, 4, 9}, {2, 3, 4, 5, 5}, {2, 3, 4, 5, 6}, {2, 3, 4, 5, 7}, {2, 3, 4, 5, 8}, {2, 3, 4, 5, 9}, {2, 3, 4, 6, 6}, {2, 3, 4, 6, 7}, {2, 3, 4, 6, 8}, {2, 3, 4, 6, 9}, {2, 3, 4, 7, 7}, {2, 3, 4, 7, 8}, {2, 3, 4, 7, 9}, {2, 3, 4, 8, 8}, {2, 3, 4, 8, 9}, {2, 3, 4, 9, 9}, {2, 3, 5, 5, 5}, {2, 3, 5, 5, 6}, {2, 3, 5, 5, 7}, {2, 3, 5, 5, 8}, {2, 3, 5, 5, 9}, {2, 3, 5, 6, 6}, {2, 3, 5, 6, 7}, {2, 3, 5, 6, 8}, {2, 3, 5, 6, 9}, {2, 3, 5, 7, 7}, {2, 3, 5, 7, 8}, {2, 3, 5, 7, 9}, {2, 3, 5, 8, 8}, {2, 3, 5, 8, 9}, {2, 3, 5, 9, 9}, {2, 3, 6, 6, 6}, {2, 3, 6, 6, 7}, {2, 3, 6, 6, 8}, {2, 3, 6, 6, 9}, {2, 3, 6, 7, 7}, {2, 3, 6, 7, 8}, {2, 3, 6, 7, 9}, {2, 3, 6, 8, 8}, {2, 3, 6, 8, 9}, {2, 3, 6, 9, 9}, {2, 3, 7, 7, 7}, {2, 3, 7, 7, 8}, {2, 3, 7, 7, 9}, {2, 3, 7, 8, 8}, {2, 3, 7, 8, 9}, {2, 3, 7, 9, 9}, {2, 3, 8, 8, 8}, {2, 3, 8, 8, 9}, {2, 3, 8, 9, 9}, {2, 3, 9, 9, 9}, {2, 4, 4, 4, 4}, {2, 4, 4, 4, 5}, {2, 4, 4, 4, 6}, {2, 4, 4, 4, 7}, {2, 4, 4, 4, 8}, {2, 4, 4, 4, 9}, {2, 4, 4, 5, 5}, {2, 4, 4, 5, 6}, {2, 4, 4, 5, 7}, {2, 4, 4, 5, 8}, {2, 4, 4, 5, 9}, {2, 4, 4, 6, 6}, {2, 4, 4, 6, 7}, {2, 4, 4, 6, 8}, {2, 4, 4, 6, 9}, {2, 4, 4, 7, 7}, {2, 4, 4, 7, 8}, {2, 4, 4, 7, 9}, {2, 4, 4, 8, 8}, {2, 4, 4, 8, 9}, {2, 4, 4, 9, 9}, {2, 4, 5, 5, 5}, {2, 4, 5, 5, 6}, {2, 4, 5, 5, 7}, {2, 4, 5, 5, 8}, {2, 4, 5, 5, 9}, {2, 4, 5, 6, 6}, {2, 4, 5, 6, 7}, {2, 4, 5, 6, 8}, {2, 4, 5, 6, 9}, {2, 4, 5, 7, 7}, {2, 4, 5, 7, 8}, {2, 4, 5, 7, 9}, {2, 4, 5, 8, 8}, {2, 4, 5, 8, 9}, {2, 4, 5, 9, 9}, {2, 4, 6, 6, 6}, {2, 4, 6, 6, 7}, {2, 4, 6, 6, 8}, {2, 4, 6, 6, 9}, {2, 4, 6, 7, 7}, {2, 4, 6, 7, 8}, {2, 4, 6, 7, 9}, {2, 4, 6, 8, 8}, {2, 4, 6, 8, 9}, {2, 4, 6, 9, 9}, {2, 4, 7, 7, 7}, {2, 4, 7, 7, 8}, {2, 4, 7, 7, 9}, {2, 4, 7, 8, 8}, {2, 4, 7, 8, 9}, {2, 4, 7, 9, 9}, {2, 4, 8, 8, 8}, {2, 4, 8, 8, 9}, {2, 4, 8, 9, 9}, {2, 4, 9, 9, 9}, {2, 5, 5, 5, 5}, {2, 5, 5, 5, 6}, {2, 5, 5, 5, 7}, {2, 5, 5, 5, 8}, {2, 5, 5, 5, 9}, {2, 5, 5, 6, 6}, {2, 5, 5, 6, 7}, {2, 5, 5, 6, 8}, {2, 5, 5, 6, 9}, {2, 5, 5, 7, 7}, {2, 5, 5, 7, 8}, {2, 5, 5, 7, 9}, {2, 5, 5, 8, 8}, {2, 5, 5, 8, 9}, {2, 5, 5, 9, 9}, {2, 5, 6, 6, 6}, {2, 5, 6, 6, 7}, {2, 5, 6, 6, 8}, {2, 5, 6, 6, 9}, {2, 5, 6, 7, 7}, {2, 5, 6, 7, 8}, {2, 5, 6, 7, 9}, {2, 5, 6, 8, 8}, {2, 5, 6, 8, 9}, {2, 5, 6, 9, 9}, {2, 5, 7, 7, 7}, {2, 5, 7, 7, 8}, {2, 5, 7, 7, 9}, {2, 5, 7, 8, 8}, {2, 5, 7, 8, 9}, {2, 5, 7, 9, 9}, {2, 5, 8, 8, 8}, {2, 5, 8, 8, 9}, {2, 5, 8, 9, 9}, {2, 5, 9, 9, 9}, {2, 6, 6, 6, 6}, {2, 6, 6, 6, 7}, {2, 6, 6, 6, 8}, {2, 6, 6, 6, 9}, {2, 6, 6, 7, 7}, {2, 6, 6, 7, 8}, {2, 6, 6, 7, 9}, {2, 6, 6, 8, 8}, {2, 6, 6, 8, 9}, {2, 6, 6, 9, 9}, {2, 6, 7, 7, 7}, {2, 6, 7, 7, 8}, {2, 6, 7, 7, 9}, {2, 6, 7, 8, 8}, {2, 6, 7, 8, 9}, {2, 6, 7, 9, 9}, {2, 6, 8, 8, 8}, {2, 6, 8, 8, 9}, {2, 6, 8, 9, 9}, {2, 6, 9, 9, 9}, {2, 7, 7, 7, 7}, {2, 7, 7, 7, 8}, {2, 7, 7, 7, 9}, {2, 7, 7, 8, 8}, {2, 7, 7, 8, 9}, {2, 7, 7, 9, 9}, {2, 7, 8, 8, 8}, {2, 7, 8, 8, 9}, {2, 7, 8, 9, 9}, {2, 7, 9, 9, 9}, {2, 8, 8, 8, 8}, {2, 8, 8, 8, 9}, {2, 8, 8, 9, 9}, {2, 8, 9, 9, 9}, {2, 9, 9, 9, 9}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 4}, {3, 3, 3, 3, 5}, {3, 3, 3, 3, 6}, {3, 3, 3, 3, 7}, {3, 3, 3, 3, 8}, {3, 3, 3, 3, 9}, {3, 3, 3, 4, 4}, {3, 3, 3, 4, 5}, {3, 3, 3, 4, 6}, {3, 3, 3, 4, 7}, {3, 3, 3, 4, 8}, {3, 3, 3, 4, 9}, {3, 3, 3, 5, 5}, {3, 3, 3, 5, 6}, {3, 3, 3, 5, 7}, {3, 3, 3, 5, 8}, {3, 3, 3, 5, 9}, {3, 3, 3, 6, 6}, {3, 3, 3, 6, 7}, {3, 3, 3, 6, 8}, {3, 3, 3, 6, 9}, {3, 3, 3, 7, 7}, {3, 3, 3, 7, 8}, {3, 3, 3, 7, 9}, {3, 3, 3, 8, 8}, {3, 3, 3, 8, 9}, {3, 3, 3, 9, 9}, {3, 3, 4, 4, 4}, {3, 3, 4, 4, 5}, {3, 3, 4, 4, 6}, {3, 3, 4, 4, 7}, {3, 3, 4, 4, 8}, {3, 3, 4, 4, 9}, {3, 3, 4, 5, 5}, {3, 3, 4, 5, 6}, {3, 3, 4, 5, 7}, {3, 3, 4, 5, 8}, {3, 3, 4, 5, 9}, {3, 3, 4, 6, 6}, {3, 3, 4, 6, 7}, {3, 3, 4, 6, 8}, {3, 3, 4, 6, 9}, {3, 3, 4, 7, 7}, {3, 3, 4, 7, 8}, {3, 3, 4, 7, 9}, {3, 3, 4, 8, 8}, {3, 3, 4, 8, 9}, {3, 3, 4, 9, 9}, {3, 3, 5, 5, 5}, {3, 3, 5, 5, 6}, {3, 3, 5, 5, 7}, {3, 3, 5, 5, 8}, {3, 3, 5, 5, 9}, {3, 3, 5, 6, 6}, {3, 3, 5, 6, 7}, {3, 3, 5, 6, 8}, {3, 3, 5, 6, 9}, {3, 3, 5, 7, 7}, {3, 3, 5, 7, 8}, {3, 3, 5, 7, 9}, {3, 3, 5, 8, 8}, {3, 3, 5, 8, 9}, {3, 3, 5, 9, 9}, {3, 3, 6, 6, 6}, {3, 3, 6, 6, 7}, {3, 3, 6, 6, 8}, {3, 3, 6, 6, 9}, {3, 3, 6, 7, 7}, {3, 3, 6, 7, 8}, {3, 3, 6, 7, 9}, {3, 3, 6, 8, 8}, {3, 3, 6, 8, 9}, {3, 3, 6, 9, 9}, {3, 3, 7, 7, 7}, {3, 3, 7, 7, 8}, {3, 3, 7, 7, 9}, {3, 3, 7, 8, 8}, {3, 3, 7, 8, 9}, {3, 3, 7, 9, 9}, {3, 3, 8, 8, 8}, {3, 3, 8, 8, 9}, {3, 3, 8, 9, 9}, {3, 3, 9, 9, 9}, {3, 4, 4, 4, 4}, {3, 4, 4, 4, 5}, {3, 4, 4, 4, 6}, {3, 4, 4, 4, 7}, {3, 4, 4, 4, 8}, {3, 4, 4, 4, 9}, {3, 4, 4, 5, 5}, {3, 4, 4, 5, 6}, {3, 4, 4, 5, 7}, {3, 4, 4, 5, 8}, {3, 4, 4, 5, 9}, {3, 4, 4, 6, 6}, {3, 4, 4, 6, 7}, {3, 4, 4, 6, 8}, {3, 4, 4, 6, 9}, {3, 4, 4, 7, 7}, {3, 4, 4, 7, 8}, {3, 4, 4, 7, 9}, {3, 4, 4, 8, 8}, {3, 4, 4, 8, 9}, {3, 4, 4, 9, 9}, {3, 4, 5, 5, 5}, {3, 4, 5, 5, 6}, {3, 4, 5, 5, 7}, {3, 4, 5, 5, 8}, {3, 4, 5, 5, 9}, {3, 4, 5, 6, 6}, {3, 4, 5, 6, 7}, {3, 4, 5, 6, 8}, {3, 4, 5, 6, 9}, {3, 4, 5, 7, 7}, {3, 4, 5, 7, 8}, {3, 4, 5, 7, 9}, {3, 4, 5, 8, 8}, {3, 4, 5, 8, 9}, {3, 4, 5, 9, 9}, {3, 4, 6, 6, 6}, {3, 4, 6, 6, 7}, {3, 4, 6, 6, 8}, {3, 4, 6, 6, 9}, {3, 4, 6, 7, 7}, {3, 4, 6, 7, 8}, {3, 4, 6, 7, 9}, {3, 4, 6, 8, 8}, {3, 4, 6, 8, 9}, {3, 4, 6, 9, 9}, {3, 4, 7, 7, 7}, {3, 4, 7, 7, 8}, {3, 4, 7, 7, 9}, {3, 4, 7, 8, 8}, {3, 4, 7, 8, 9}, {3, 4, 7, 9, 9}, {3, 4, 8, 8, 8}, {3, 4, 8, 8, 9}, {3, 4, 8, 9, 9}, {3, 4, 9, 9, 9}, {3, 5, 5, 5, 5}, {3, 5, 5, 5, 6}, {3, 5, 5, 5, 7}, {3, 5, 5, 5, 8}, {3, 5, 5, 5, 9}, {3, 5, 5, 6, 6}, {3, 5, 5, 6, 7}, {3, 5, 5, 6, 8}, {3, 5, 5, 6, 9}, {3, 5, 5, 7, 7}, {3, 5, 5, 7, 8}, {3, 5, 5, 7, 9}, {3, 5, 5, 8, 8}, {3, 5, 5, 8, 9}, {3, 5, 5, 9, 9}, {3, 5, 6, 6, 6}, {3, 5, 6, 6, 7}, {3, 5, 6, 6, 8}, {3, 5, 6, 6, 9}, {3, 5, 6, 7, 7}, {3, 5, 6, 7, 8}, {3, 5, 6, 7, 9}, {3, 5, 6, 8, 8}, {3, 5, 6, 8, 9}, {3, 5, 6, 9, 9}, {3, 5, 7, 7, 7}, {3, 5, 7, 7, 8}, {3, 5, 7, 7, 9}, {3, 5, 7, 8, 8}, {3, 5, 7, 8, 9}, {3, 5, 7, 9, 9}, {3, 5, 8, 8, 8}, {3, 5, 8, 8, 9}, {3, 5, 8, 9, 9}, {3, 5, 9, 9, 9}, {3, 6, 6, 6, 6}, {3, 6, 6, 6, 7}, {3, 6, 6, 6, 8}, {3, 6, 6, 6, 9}, {3, 6, 6, 7, 7}, {3, 6, 6, 7, 8}, {3, 6, 6, 7, 9}, {3, 6, 6, 8, 8}, {3, 6, 6, 8, 9}, {3, 6, 6, 9, 9}, {3, 6, 7, 7, 7}, {3, 6, 7, 7, 8}, {3, 6, 7, 7, 9}, {3, 6, 7, 8, 8}, {3, 6, 7, 8, 9}, {3, 6, 7, 9, 9}, {3, 6, 8, 8, 8}, {3, 6, 8, 8, 9}, {3, 6, 8, 9, 9}, {3, 6, 9, 9, 9}, {3, 7, 7, 7, 7}, {3, 7, 7, 7, 8}, {3, 7, 7, 7, 9}, {3, 7, 7, 8, 8}, {3, 7, 7, 8, 9}, {3, 7, 7, 9, 9}, {3, 7, 8, 8, 8}, {3, 7, 8, 8, 9}, {3, 7, 8, 9, 9}, {3, 7, 9, 9, 9}, {3, 8, 8, 8, 8}, {3, 8, 8, 8, 9}, {3, 8, 8, 9, 9}, {3, 8, 9, 9, 9}, {3, 9, 9, 9, 9}, {4, 4, 4, 4, 4}, {4, 4, 4, 4, 5}, {4, 4, 4, 4, 6}, {4, 4, 4, 4, 7}, {4, 4, 4, 4, 8}, {4, 4, 4, 4, 9}, {4, 4, 4, 5, 5}, {4, 4, 4, 5, 6}, {4, 4, 4, 5, 7}, {4, 4, 4, 5, 8}, {4, 4, 4, 5, 9}, {4, 4, 4, 6, 6}, {4, 4, 4, 6, 7}, {4, 4, 4, 6, 8}, {4, 4, 4, 6, 9}, {4, 4, 4, 7, 7}, {4, 4, 4, 7, 8}, {4, 4, 4, 7, 9}, {4, 4, 4, 8, 8}, {4, 4, 4, 8, 9}, {4, 4, 4, 9, 9}, {4, 4, 5, 5, 5}, {4, 4, 5, 5, 6}, {4, 4, 5, 5, 7}, {4, 4, 5, 5, 8}, {4, 4, 5, 5, 9}, {4, 4, 5, 6, 6}, {4, 4, 5, 6, 7}, {4, 4, 5, 6, 8}, {4, 4, 5, 6, 9}, {4, 4, 5, 7, 7}, {4, 4, 5, 7, 8}, {4, 4, 5, 7, 9}, {4, 4, 5, 8, 8}, {4, 4, 5, 8, 9}, {4, 4, 5, 9, 9}, {4, 4, 6, 6, 6}, {4, 4, 6, 6, 7}, {4, 4, 6, 6, 8}, {4, 4, 6, 6, 9}, {4, 4, 6, 7, 7}, {4, 4, 6, 7, 8}, {4, 4, 6, 7, 9}, {4, 4, 6, 8, 8}, {4, 4, 6, 8, 9}, {4, 4, 6, 9, 9}, {4, 4, 7, 7, 7}, {4, 4, 7, 7, 8}, {4, 4, 7, 7, 9}, {4, 4, 7, 8, 8}, {4, 4, 7, 8, 9}, {4, 4, 7, 9, 9}, {4, 4, 8, 8, 8}, {4, 4, 8, 8, 9}, {4, 4, 8, 9, 9}, {4, 4, 9, 9, 9}, {4, 5, 5, 5, 5}, {4, 5, 5, 5, 6}, {4, 5, 5, 5, 7}, {4, 5, 5, 5, 8}, {4, 5, 5, 5, 9}, {4, 5, 5, 6, 6}, {4, 5, 5, 6, 7}, {4, 5, 5, 6, 8}, {4, 5, 5, 6, 9}, {4, 5, 5, 7, 7}, {4, 5, 5, 7, 8}, {4, 5, 5, 7, 9}, {4, 5, 5, 8, 8}, {4, 5, 5, 8, 9}, {4, 5, 5, 9, 9}, {4, 5, 6, 6, 6}, {4, 5, 6, 6, 7}, {4, 5, 6, 6, 8}, {4, 5, 6, 6, 9}, {4, 5, 6, 7, 7}, {4, 5, 6, 7, 8}, {4, 5, 6, 7, 9}, {4, 5, 6, 8, 8}, {4, 5, 6, 8, 9}, {4, 5, 6, 9, 9}, {4, 5, 7, 7, 7}, {4, 5, 7, 7, 8}, {4, 5, 7, 7, 9}, {4, 5, 7, 8, 8}, {4, 5, 7, 8, 9}, {4, 5, 7, 9, 9}, {4, 5, 8, 8, 8}, {4, 5, 8, 8, 9}, {4, 5, 8, 9, 9}, {4, 5, 9, 9, 9}, {4, 6, 6, 6, 6}, {4, 6, 6, 6, 7}, {4, 6, 6, 6, 8}, {4, 6, 6, 6, 9}, {4, 6, 6, 7, 7}, {4, 6, 6, 7, 8}, {4, 6, 6, 7, 9}, {4, 6, 6, 8, 8}, {4, 6, 6, 8, 9}, {4, 6, 6, 9, 9}, {4, 6, 7, 7, 7}, {4, 6, 7, 7, 8}, {4, 6, 7, 7, 9}, {4, 6, 7, 8, 8}, {4, 6, 7, 8, 9}, {4, 6, 7, 9, 9}, {4, 6, 8, 8, 8}, {4, 6, 8, 8, 9}, {4, 6, 8, 9, 9}, {4, 6, 9, 9, 9}, {4, 7, 7, 7, 7}, {4, 7, 7, 7, 8}, {4, 7, 7, 7, 9}, {4, 7, 7, 8, 8}, {4, 7, 7, 8, 9}, {4, 7, 7, 9, 9}, {4, 7, 8, 8, 8}, {4, 7, 8, 8, 9}, {4, 7, 8, 9, 9}, {4, 7, 9, 9, 9}, {4, 8, 8, 8, 8}, {4, 8, 8, 8, 9}, {4, 8, 8, 9, 9}, {4, 8, 9, 9, 9}, {4, 9, 9, 9, 9}, {5, 5, 5, 5, 5}, {5, 5, 5, 5, 6}, {5, 5, 5, 5, 7}, {5, 5, 5, 5, 8}, {5, 5, 5, 5, 9}, {5, 5, 5, 6, 6}, {5, 5, 5, 6, 7}, {5, 5, 5, 6, 8}, {5, 5, 5, 6, 9}, {5, 5, 5, 7, 7}, {5, 5, 5, 7, 8}, {5, 5, 5, 7, 9}, {5, 5, 5, 8, 8}, {5, 5, 5, 8, 9}, {5, 5, 5, 9, 9}, {5, 5, 6, 6, 6}, {5, 5, 6, 6, 7}, {5, 5, 6, 6, 8}, {5, 5, 6, 6, 9}, {5, 5, 6, 7, 7}, {5, 5, 6, 7, 8}, {5, 5, 6, 7, 9}, {5, 5, 6, 8, 8}, {5, 5, 6, 8, 9}, {5, 5, 6, 9, 9}, {5, 5, 7, 7, 7}, {5, 5, 7, 7, 8}, {5, 5, 7, 7, 9}, {5, 5, 7, 8, 8}, {5, 5, 7, 8, 9}, {5, 5, 7, 9, 9}, {5, 5, 8, 8, 8}, {5, 5, 8, 8, 9}, {5, 5, 8, 9, 9}, {5, 5, 9, 9, 9}, {5, 6, 6, 6, 6}, {5, 6, 6, 6, 7}, {5, 6, 6, 6, 8}, {5, 6, 6, 6, 9}, {5, 6, 6, 7, 7}, {5, 6, 6, 7, 8}, {5, 6, 6, 7, 9}, {5, 6, 6, 8, 8}, {5, 6, 6, 8, 9}, {5, 6, 6, 9, 9}, {5, 6, 7, 7, 7}, {5, 6, 7, 7, 8}, {5, 6, 7, 7, 9}, {5, 6, 7, 8, 8}, {5, 6, 7, 8, 9}, {5, 6, 7, 9, 9}, {5, 6, 8, 8, 8}, {5, 6, 8, 8, 9}, {5, 6, 8, 9, 9}, {5, 6, 9, 9, 9}, {5, 7, 7, 7, 7}, {5, 7, 7, 7, 8}, {5, 7, 7, 7, 9}, {5, 7, 7, 8, 8}, {5, 7, 7, 8, 9}, {5, 7, 7, 9, 9}, {5, 7, 8, 8, 8}, {5, 7, 8, 8, 9}, {5, 7, 8, 9, 9}, {5, 7, 9, 9, 9}, {5, 8, 8, 8, 8}, {5, 8, 8, 8, 9}, {5, 8, 8, 9, 9}, {5, 8, 9, 9, 9}, {5, 9, 9, 9, 9}, {6, 6, 6, 6, 6}, {6, 6, 6, 6, 7}, {6, 6, 6, 6, 8}, {6, 6, 6, 6, 9}, {6, 6, 6, 7, 7}, {6, 6, 6, 7, 8}, {6, 6, 6, 7, 9}, {6, 6, 6, 8, 8}, {6, 6, 6, 8, 9}, {6, 6, 6, 9, 9}, {6, 6, 7, 7, 7}, {6, 6, 7, 7, 8}, {6, 6, 7, 7, 9}, {6, 6, 7, 8, 8}, {6, 6, 7, 8, 9}, {6, 6, 7, 9, 9}, {6, 6, 8, 8, 8}, {6, 6, 8, 8, 9}, {6, 6, 8, 9, 9}, {6, 6, 9, 9, 9}, {6, 7, 7, 7, 7}, {6, 7, 7, 7, 8}, {6, 7, 7, 7, 9}, {6, 7, 7, 8, 8}, {6, 7, 7, 8, 9}, {6, 7, 7, 9, 9}, {6, 7, 8, 8, 8}, {6, 7, 8, 8, 9}, {6, 7, 8, 9, 9}, {6, 7, 9, 9, 9}, {6, 8, 8, 8, 8}, {6, 8, 8, 8, 9}, {6, 8, 8, 9, 9}, {6, 8, 9, 9, 9}, {6, 9, 9, 9, 9}, {7, 7, 7, 7, 7}, {7, 7, 7, 7, 8}, {7, 7, 7, 7, 9}, {7, 7, 7, 8, 8}, {7, 7, 7, 8, 9}, {7, 7, 7, 9, 9}, {7, 7, 8, 8, 8}, {7, 7, 8, 8, 9}, {7, 7, 8, 9, 9}, {7, 7, 9, 9, 9}, {7, 8, 8, 8, 8}, {7, 8, 8, 8, 9}, {7, 8, 8, 9, 9}, {7, 8, 9, 9, 9}, {7, 9, 9, 9, 9}, {8, 8, 8, 8, 8}, {8, 8, 8, 8, 9}, {8, 8, 8, 9, 9}, {8, 8, 9, 9, 9}, {8, 9, 9, 9, 9}, {9, 9, 9, 9, 9}=1,287 combinations!!!.

Katie wants to hang crepe paper on the 4 sides of the square and on the 2 diagonals.

side length of the square  =  15 ft

diagonal length of square   =   \(\sqrt{15^2+15^2}\)    ft 

diagonal length of square   =   \(\sqrt{2\cdot15^2}\)          ft

diagonal length of square   =   \(\sqrt2\cdot\sqrt{15^2}\)      ft

diagonal length of square   =   \(15\sqrt2\)          ft

Assuming that none of the crepe paper will hang down at all, that it will be flat against the ceiling....

length of crepe paper needed   =   4( side length of square )  +  2( diagonal length of square )

length of crepe paper needed   =   4( 15 ft )  +  2( 15√2 ft )

length of crepe paper needed   =   60 ft  +  30√2 ft

length of crepe paper needed   ≈   102.426  ft

20  ft  =  1  roll

1  ft   =   1/20  roll

102.426  ft  =  102.426/20   rolls

102.426  ft  ≈  5.121   rolls

So she needs to buy  5.121  rolls of paper.  But since she probably can't buy a fraction of a roll,  and she probably wants the paper to hang down some, she needs to buy at least  6  rolls.

* edited to correct an error!!! *

If this is what your teacher meant:  ∑(98-2n), n=1 to 11, then it sums up to = 946.

I know it may seem that way, but this was all that was apart of the question. I don't know why, my teacher set it up this way

\(\log_{4}3=x$. Then $\log_{2}27=kx\)       find k

In exponential form we have.....

4^x  = 3           and        2^(kx) = 27

Working with the expression on  the left :

4^x  = 3      and we can write

(2^2)^x  = 3

2^(2x)  = 3

Cube each side

[ 2^(2x)]^3  = 3^3

2^(6x)  =  27

So  k  = 6

Ths base is opposite the 30° angle

The height is opposite the 60°  angle  and  is √3 as long as the base =  5√3  units

So.....the area  = (1/2) base * height  =

(1/2) (5) *(5√3)  =

12.5√3  units^2   ≈  21.7 units^2

We will have a right triangle , here....the hypotenuse is 12   and the side opposite the angle of interest will be 11.8

So....we have the opposite side and the hypotenuse.....

To    find this angle.....use the   sine inverse (arcsin)....so we have

arcsin (11.8 / 12)  =  79.52°

So...not safe  !!!!

Here's a pic: 

\( \frac{5}{24} + \left|x-\frac{11}{48}\right| < \frac{5}{16}\)

subtract 5/24 from both sides

l x - 11/48  l  < 5/16 - 5/24

l x - 11/48 l  <  15/48 - 10/48

l x -  11/48 l  <  5/48        we have two equations, here

x - 11/48 < 5/48            x  - 11/48 >  - 5/48

                          add  11/48 to  both sides

x < 16/48                   x  > 6/48

x < 1/3                x > 1/8

x  = ( 1/8 ,  1/3)

What is it in interval notation?

What are the probabilities of coming up  heads and talls???....they aren't showing up for me...

I'm pretty sure that this equation is missing some things. 

First of all, a sigma notation must have a range, from n=x to k

This is missing the range, so this problem is undoable.

I can help you if you repost with the missing values. 

We first need to find the area of the shaded region. 

The width is 3 + 1 + 2 = 6 

The length is 2 * 5 = 10

The total area of this rectangle is 6 * 10 = 60 

The shaded region has a total area of: 

3 * 2 + 2 * 2 + 2 * 1 = 12 

The part of the rectangle that is not shaded must be 60 - 12 = 48

The probabilty is 48/60 = 4/5 = 0.8 = 80%

Yay! I like that we have the same answer. This was hard, was wondering if I was right...

Oh my god! Happy Birthday Melody. Thank you for all the contributions to this amazing math website. I wish you the best day ever!

I don't know how to insert images or program in desmos as well as hectictar, but still, happy birthday!!!

:) 

3. 

1/3 < x < 1/8

2. √(10p) * √(5p^2) * √(6p^4)

= √(300p^7)

= 10p^3√(3p)

1. log₉(2x-7)=1.5

log_ab = c means that a^c = b

So this equation means that:

9 to the power of 1.5 is equal to (2x-7)

9^1.5 = 2x - 7 

Since 9^1.5 = 27, 2x - 7 = 27

Solving for x, we have that x = 17.

What hectictar said  !!!!

Here's a cake.....!!!

The answer is  given by :

[ First term + Last term] * 10 / 2

The frist term is 14

The last  is  14 + 3(10 -1)  =  14 + 3(9) =  41    ....  so  we have.......

[ 14 + 41 ] * 10 / 2  =

[55 * 10]  / 2  =

$275

P(Both Even )  =   (2/5) (1/4)  =  2/20  =  1/10

P(Both Prime)  = (3/5)(2/4) =  6/20  =  3/10

P (sum of two numbers is odd)  ....we have C(5,2)  = 10 possible sets

Sets where the sum of two integers is odd :

(1,2) (1,4)

(2,3) (2,5)

(3, 4) 

So...P (Sum of two numbers is odd) =  5/10   =  1/2

P (Product of two numbers is odd)

(1,3) (1,5)

(3, 5)

So.....P (Product of two numbers is odd)  = 3 / 10

It seems  that   "John" and "Bob"  have somehow morphed into "Grogg"  and "Winnie"...

But, anyway.....call the number of minutes that  one of tthem could be late  = x

And call the number of minutes that the other could be late  = y

So......the total possible minutes that they could be late is 60 minutes each...so...we have this equation of a line

x + y  ≤  120    (1)

But....we  are looking for this  x + y  ≤ 45    (2)

Look at the graph here : https://www.desmos.com/calculator/90isasjiab

The area  of the triangle formed by (1)  in the first quadrant is  (1/2)base * height =

(1`/ 2) (120) (120)   =  14400 / 2 =  7200 units^2

The area  of (2)  in the first quadrant  is   (1/2)(45) (45)  = 1012.5 units^2

So....the probability  that the sum of the minutes that both are late is ≤ 45  is

1012.5 / 7200   =    9 / 64

In order to dilate a point about a center of dilation that is not the origin, I would recommend manipulating the current Cartesian plane where the origin lies at the center of dilation. 

For example, if we translate the entire coordinate plane by the rule \((x,y)\Rightarrow (x-1,y-2)\), then the center of dilation becomes the origin, and the point (4,7), after the translation has occurred, transforms to (3,5). 

We can now dilate the point like normal because the origin is now the center of dilation. I can now use the scale factor where the dilated point can be determined as \((x,y)\Rightarrow (kx,ky)\) , where k, 10 in this case, is the scale factor.

Therefore,\((3,5)\Rightarrow(10*3,10*5)=(30,50)\).

We aren't done yet, though! Remember the translation we did at the beginning? We have to undo this action to determine the true location on the real Cartesian plane. Let's translate \((x,y)\Rightarrow(x+1,y+2)\) to undo the previous translation. Therefore, \((30,50)\Rightarrow (31,52)\) , or the second option listed.

Last one

P(Red )  =  25 / ( 25 + 95)  = 25/120

P(Blue)  =  95 / 120

These events are complementary because  25/120 + 95 / 120  =  120 / 120  =  1

P (L l R)  =  P(L and R) / P(R)

Rearranging this, we have

P(R)  =  P(L and R)  / P(L l R )

P(R)  = 0.03  / 0.0625

Second one

P(Single l Has Pet )  =  16 / (16 + 24)  =  16/40   =  2/5  = .40

P (Single l Has No Pet )  = 12 /  (18 + 12)  = 12 / 30  = 2/5  = .40 true

P (Married l Has No Pet )  = 18 / (18 + 12)  = 18 /30 = 3/5  = .60

P(Married l Has Pet )  = 24 / ( 24 + 16)  = 24 / 40  =  3/5  = .60  true

RP....I believe that   C  is correct for the last one....for instance

If P( Q)  = .30     and P (T)  =  .40

Then

P(Q l T)  =  P (Q and T ) / P(T)  =   .12/ .40  = 0.3

But

P( T l Q )  = P(Q and T) / P(Q)  = .12 / .30  = 0.4

First one :

a_n  = 1500 (1.15)^n-1

Second one....note the terms

7 (-4)^n-1

7, -28,  112 , -448, etc...

an   =  -4 a_n-1  , a₁  = 7