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Question

Fifteen people took part in a chess competition. Every player plays with other players once. Find the number of games played in the tournament

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Solution

Total number of people available for chess competition =15
Number of people needed to play a chess game =2

We need to choose 2 different people from 15 people for each chess game.

The number of games played would be 15C2.

Here, n=15 and r=2.

15C2=15!2!(152)! ( nCr=n!r!(nr)!)

15C2=15!2!13!

15C2=15×14×13!2!13!

15C2=15×142×1

15C2=15×7
15C2=105

The number of games played if every person must play each of the others is 105.

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