The personnel manager for a commercial bank has interviewed five men and seven women for four managerial training positions available with her bank. If the final selection will include two men and two women, how many different combinations are possible?

Any suggestions will help.

I am thinking it is 4 because that is what 2 squared equals... the number of the final selection.

Are you sure its 4? At first glance I thought it was 4, but there are no other outcomes are there? So I get 3

Man, man
Woman, man
Woman, woman

Good point. Yep. Its 3. I was thinking woman, man... man, woman... but that is the same. So yep. Its 3.

Then I wonder why my answer is 210??

210? I got 5.3:confused:

The answer is 210.

C(5,2)*C(7,2)=210

The personnel manager for a commercial bank has interviewed five men and seven women for four managerial training positions available with her bank. If the final selection will include two men and two women, how many different combinations are possible?

Any suggestions will help.
Man, man, woman, woman
-or-
Man, woman, man, woman
-or-
Man, woman, woman, man
-or-
Woman, woman, man, man
-or-
Woman, man, woman, man
-or-
Woman, man, man, woman

Did I miss any combonations of two and two?

Yes, about 204 of them :)

The men and women are distinct. They are different individuals, not just a man and a woman.

Thank you, all!