Throwing golf balls for teams

[jbc]

Please can somebody help with this.

8 of us usually play golf on a Saturday. Before we play we throw balls to see who will play with each other - 2 groups of 4 are chosen by taking those balls that lie closest to each other after they have been thrown. My question is this:

What is the probability that 2 specific people will randomly fall into the same group of 4 players from the initial sample of 8?

 

[Dason]

There are \(\binom{8}{4}\) different ways to split up into two groups of 4 each. Once you pick the specific pair you have in mind there are \(\binom{6}{2}\) ways to choose the remaining 2 people in the group. So the probability that those two specific people end up together is \(\frac{\binom{6}{2}}{\binom{8}{4}}\)