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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

1. 90
2. 120
3. 140
4. 105

### 1 comment

Any one explain this one please..

let we have seven men as a,b,c,d,e,f,g

we have to pick 2 men to form a pair

no. of ways to pick 2 men from 7 = C(7,2)

=21 pairs

after picking 2 men from 7 people we are left with 5 men's , again we need one more pair to play

so it can be done in C(5,2) = 10 ways

total = 21*10

=210

now if ab is picked and played against cd similarly cd is picked and plays against ab

order does not matter for each pair

so total games played = 210/2

=105
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