In an badminton club,there are 10 couples.They will play mixed doubles match.The condition is that the wives will not play with their husbands and also they will not oppose them.Find out the number of matches possible?

The answer is (10*8)*(9*7)

• For each match we need two ladies and two men.

• Let us from the ten ladies select two ladies = 10c2

• now out of the 10 men we are not allowed to select the husbands of these ladies so we have 8 choices left out of which 2 need to be selected = 8c2
• Let the ladies selected be l₁ and l₂ and the men selected be m₁ and m₂ in one particular case then among the selctions we can form two matches as each lady can go with any of the two men.

therefore total no. of matches = 10c2 * 8c2 * 2