Variation on the birthday problem

Hi All,

Suppose a randomly selected group of $\textit{k}$ people are brought together. What is the probability that exactly one pair has the same birthday?

The solution is ${k\choose{2}} \cdot \left( 365 \cdot 364 \cdots(365-k+2) \over 365^k \right)$

But I'm can't see exactly why this is so. Any help much appreciated. MD