1993 TYS

A tennis club has $n$ male players and $n$ female players. For a tournament the players are to be arranged in $n$ pairs, with each pairing consisting of one male and one female. Find the number of possible pairings.

In the state of Utopia, the alphabet contains $25$ letters. A car registration number consists of two different letters of the alphabet followed by an integer $n$ such that $100\le n\le 999$.

Find the number of possible car registration numbers.