SOLUTION: A die is rolled 4 times. find the probability of two 1's, one 2, and one 3.

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Question 464204: A die is rolled 4 times. find the probability of two 1's, one 2, and one 3.
Answer by Edwin McCravy(20064) About Me  (Show Source):
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A die is rolled 4 times. find the probability of 
two 1's, one 2, and one 3.

The probability of rolling the sequence 1,1,2,3 is %281%2F6%29%5E4=1%2F1296.

But that sequence could be in any order, and the 
number of ways of arranging 1,1,2,3 since the 
two 1's are indistinguishable, is 4%21%2F2%21=24%2F2=12

Therefore the desired probability is 12%2Aexpr%281%2F1296%29=12%2F1296=1%2F108. 


Edwin