maths question permutation and combination

[sunny2009]

there are 4 married couples in a club.a 3 member committee must be formed from among them,such that no married couple is part of the committee.
in how many ways,this commitee can be formed?
plzzz someone...explain in detail.

[duck]

Hi Sunny.. :)

We have 4 married couples. So, 4 males and 4 females.
We need to select a committee of 3 people such that no couple should be a part of it.
Now, it can be done in the following way:
 Selecting 3 males out of 4 = 4C3
+ Selecting 3 females out of 4 = 4C3
+ Selecting 2 males out of 4 and 1 female out of 2 ( since , only 2 women will be left whose husbands are not selected) = 4C2*2C1
+ selecting 2 females out of 4 and 1 male out of 2 ( since, only 2 males will be left whose wives are not selected) = 4C2*2C1

= 32 ways

[sunny2009]

hello duck :):)
thank u so much.i understood it very nicely.