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.
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
