N1993 P1 Q10

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.