A standard six-sided die is rolled 5 times. You are told that among the rolls, there was one 4 one 5 and three 6's. How many possible sequences of rolls could there have been? (For example, 6,5,6,6,4 is one possible sequence.)
There are C(5,3) = 10 ways to choose the position of the 3s, then C(5,1) = 5 ways to choose the position of the 4, and C(5,1) = 5 ways to choose the position of the 1, so the number of sequences is 10*5*5 = 250.
You should have 20 DISTINCT permutations as follows:
{4, 5, 6, 6, 6}, {4, 6, 5, 6, 6}, {4, 6, 6, 5, 6}, {4, 6, 6, 6, 5}, {5, 4, 6, 6, 6}, {5, 6, 4, 6, 6}, {5, 6, 6, 4, 6}, {5, 6, 6, 6, 4}, {6, 4, 5, 6, 6}, {6, 4, 6, 5, 6}, {6, 4, 6, 6, 5}, {6, 5, 4, 6, 6}, {6, 5, 6, 4, 6}, {6, 5, 6, 6, 4}, {6, 6, 4, 5, 6}, {6, 6, 4, 6, 5}, {6, 6, 5, 4, 6}, {6, 6, 5, 6, 4}, {6, 6, 6, 4, 5}, {6, 6, 6, 5, 4} = 20 permutations.
