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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.)

Jan 3, 2020

#1
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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.

Jan 3, 2020
#2
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Hmm, it's incorrect. Try again.

Guest Jan 3, 2020
#3
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To find the sequences of rolls, we need to find the ways to arrange the numbers 6,4,6,6,5 where the 6s are indistinguishable. You should be able to follow through.

Guest Jan 3, 2020
#4
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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.

Jan 3, 2020