Ben rolls four fair 10-sided dice. What is the probability that exactly three of the dice show a prime number?
There are: 10^4 ==10,000 4-digit permutations with repeats.
Since there are only 4 prime numbers < 10, then you have:
6 choices for the first place
4 choices for the 3rd place
3 choices for the 2nd place
2 choices for the 1st place.
6 x 4 x 3 x 2 ==144. Then the 4 primes taken 3 at a time gives us:
4 C 3 ==4 and: 144 x 4 ==576 permutations with at least 3 primes. But, there are:4! permutations which have 4 primes, and since we want EXACTLY 3 primes, then we have:
576 - 4! ==576 - 24 ==552 permutations with exactly 3 primes.
