## Question

In a class tournament when the participants were to play one game with another, two class players fell ill, having played 3 games each (*not played between them*). If the total number of games played is 84, the number of participants at the beginning was:

### Solution

15

Let no. of participants at the beginning were *n*.

Now, left players are *n* – 2

According to question :

^{n – 2}C_{2} + 3 + 3 = 84

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