##### Number of games to play

For a game in which 2 partners oppose 2 other partners, seven men are available. If every possible pair must play against every other pair, then the number of games to be played is

- 90
- 120
- 140
- 105

**Answer**

Let us consider 7 men as a, b, c, d, e, f ,g

Then no. of ways to pick 2 out of 7 men = ^{7}C_{2} = 21

Then no. of ways to pick 2 out of remaining 5 men = ^{5}C_{2} =10

thus , total possible way of game =21*10/2 =210/2 = 105

//we have divided it by 2 as playing pair a with pair b , is same as playing pair b with pair a

Ans is 105

there will be 7C2 =21 possible pair(of 2). As each pair again play against each other, also in this 21 pairs . If we directly do 21C26 , there will be some pair of 2 which contain same player which play against the other pair in which he is also one member, so it is wrong so we have to remove this redundancy. there will be 6 such pair. So 21-6=15 . So from 15 such distinct pair , there will be 15C2 = 105 total matches.