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# Combinations with repeats.....

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Out of the natural numbers 1 - 9 (nine numbers), how many combinations(NOT permutations) of 5-digit numbers are possible with repeats allowed such as: 12345, 11234, 11123, 11112, 11111....etc. Any help would be appreciated. Thank you.

Apr 15, 2018
edited by Guest  Apr 15, 2018

#1
0

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!!!.

Apr 16, 2018
edited by Guest  Apr 16, 2018
#2
0

To give you a better understanding of this, consider 5 letters of the alphabet taken 3 at a times with desired repeats. a, b, c, d, e =[5+3 - 1]C3 =7C3 =35 combinations with repeats as follows:

{a, a, a} | {a, a, b} | {a, a, c} | {a, a, d} | {a, a, e} | {a, b, b} | {a, b, c} | {a, b, d} | {a, b, e} | {a, c, c} | {a, c, d} | {a, c, e} | {a, d, d} | {a, d, e} | {a, e, e} | {b, b, b} | {b, b, c} | {b, b, d} | {b, b, e} | {b, c, c} | {b, c, d} | {b, c, e} | {b, d, d} | {b, d, e} | {b, e, e} | {c, c, c} | {c, c, d} | {c, c, e} | {c, d, d} | {c, d, e} | {c, e, e} | {d, d, d} | {d, d, e} | {d, e, e} | {e, e, e} (total: 35) - combinations.

Apr 16, 2018