Committee of 3M and 3W.

[santhoshsram]

Company X has 6 regional offices. Each regional office must recommend 2 candidate, one male and one female, to serve on the auditing committee. If each of the offices must be represented by exactly one member on the auditing committee and if the committee must consist of an equal number of male and female employees, how many different committees can be formed?

[[email protected]]

I think ans is 6!/Square of (3!)=20
There is 6M & 6F, so to form equal no. of male and equal no. of female in the committee we must have 3M & 3F in the committie.
Now 3M can be chosen from 6M in 6C3 ways i.e,6!/Square of (3!). Now, we have selected 3M and there is no choice left as to which women we must select since each office can represenet 1M & 1F.

[santhoshsram]

[spoiler]Spot On! I used a different approach though.
We know there have to be 3M and 3F. Each of the offices can send either an M or F. So the number of different committees will be the number of ways of arranging MMMFFF. Which is 6!/(3!x3!).
[/spoiler]

I think ans is 6!/Square of (3!)=20
There is 6M & 6F, so to form equal no. of male and equal no. of female in the committee we must have 3M & 3F in the committie.
Now 3M can be chosen from 6M in 6C3 ways i.e,6!/Square of (3!). Now, we have selected 3M and there is no choice left as to which women we must select since each office can represenet 1M & 1F.