*Source: Pólya & Kilpatrick 1974* 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.