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Question

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :
  1. (15C1)2+(14C1)2+....+(1C1)2
  2. 15!
  3. 15(15C1×15C1)
  4. 15C1×15!


Solution

The correct option is B 15!
We have to select 15 teams and every team consists of one man and one woman.

total man =15, total woman =15

Consider all the 15 man as group A and all 15 woman as group B,now we have to make 15 teams taking one member from group A and one member from group B.

Now consider one member from group A, he has 15 options to pair up with one member of group B,next member from group A has 14 to pair up with group B,third member will have 13 options and so on.

So the total no. of ways of selecting 15 teams is
=15×14×13.....×1=15!

 

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