Here, is a problem on counting. Read it and crack it before you compare your solution with the one I present !!!

In a tennis tournament, there are 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

different ways.

Solution.

Call the required number of pairings of players . If you are a participant, you can be matched with any one of  the other players. Once your antagonist is chosen, there remain

players who  can be paired in ways. Hence,

.

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Nalin Pithwa