This is straight from the probability and combinatorics book- but its a practice problem and there is no explanation in the back..

What is the probability of getting exactly two 6's on three rolls of a fair die?

Thanks!

There are 6*6*6 = 216 possible outcomes.

There are 3 general ways to exactly 2 6's:

66x
6x6
x66

where x = one of the other numbers: 1,2,3,4, or 5

there are 5 ways to get each of the above for example: 661, 662, 663, 664, 665

there are 5 * 3 = 15 ways to get exactly 2 sixes

so, the probability is 15/216

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