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Ben rolls four fair 10-sided dice. What is the probability that exactly three of the dice show a prime number?

 Oct 8, 2021
 #1
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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.

 Oct 9, 2021
 #2
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The probability is:552 / 10,000==5.52%

Guest Oct 9, 2021

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