Tennis Tournaments

Player Pairing

I stumbled onto this elegant problem in The Stanford Mathematics Problem Book:

In a tennis tournament there are 2n participants. In the first round of the tournament each participant plays just once, so there are n games, each occupying a pair of players. Show that the pairing for the first round can be arranged in exactly

\(1 × 3 × 5 × 7 × 9... × (2n - 1)\)

different ways.

Have fun !