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Six 6-sided dice are rolled. What is the probability that exactly two of the dice show a 1 and exactly three of the dice show a 2? Express your answer as a common fraction.

 Oct 14, 2020
 #1
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It is much easier and simpler to list the "combinations" first and then calculate the "permutations" as follows:

 

112223 , 112224 , 112225 , 112226 , Total =  4 combinations.

 

Each of the above combinations has: 6! / [2! * 3!] =60 permutations

 

And the probability is: [4 x 60] = 240 / 6^6 =5 / 972

 
 Oct 14, 2020
 #2
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You can also do it mathematically as follows:

 

[6C2] * [4C3] * 4 =15 * 4 * 4 = 240 / 6^6 = 5 / 972 - which is same probability.

 
 Oct 14, 2020

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