(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If Sam and Peter are among n men who are arranged at random in a line, what is the probability that exactly k men stand between them?"

2. Relevant equations

Not sure.

3. The attempt at a solution

This is driving me insane. I listed out the possibilities for n = 3, and it looked to me like Peter and Sam could surround n men

2(n-k-1)

ways. Since there are n! possible lines, I said:

p = 2(n-k-1)/n!

But the book says

p = 2(n-k-1)/n(n-1)

The frustrating thing is that our answers are equal for n=3, but obviously not for higher values of n. I started trying to do it concretely for n=4, but there were so many possibilities that I got too confused.

It's just killing me, because I know the formula I came up with for n=3 was just a guess based on my empirical observation of the outcomes. I don't know how to do this problem "theoretically."

What am I doing wrong?

Thanks.

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# Homework Help: Cominatorial Probability

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