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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 27, 2020
 #1
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6C2 * 4C3 * 4 == 240 / 6^6 == 5 / 972

 Oct 27, 2020
 #2
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You can also verify it this way:

 

1 - Calculate ALL the "combinations" first, then convert the "combinations" into "permutations":

The combinations are: 112223,  112224,  112225,  112226.

 

Each combination has this many permutations: 6! / [2!.3!] =720 / 12 =60 permutations each.

 

60  x  4 = 240 / 6^6 = 5 /972

 Oct 27, 2020

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