Difficult question

[gmatuser100]

Question:
=================
Company X has n regional offices, where n represents an even integer. Each regional office must recommend two candidates, one male and one female, to serve on the corporate 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?

[RR]

I doubt if this is a GMAT Prep qn, but if it is then plz post the full qn with answer choices. Anyway, will give it a shot.
Company has n offices and from each office one male and one female will be recommended. Hence there will be n males and n females who will be recommended.
Each office must be represented by exactly one member which implies that totally only n people will be elected to the committee.
Also, there must be equal number of men and women which means that there must be n/2 men and n/2 women.

So out of n men, n/2 should be selected
and out of n women, n/2 should be selected.

Total ways of doing that

nC(n-2) x nC(n-2)
=
n!^2
----------
(n/2)!^4

[RonPurewal]

I doubt if this is a GMAT Prep qn, but if it is then plz post the full qn with answer choices. Anyway, will give it a shot.
Company has n offices and from each office one male and one female will be recommended. Hence there will be n males and n females who will be recommended.
Each office must be represented by exactly one member which implies that totally only n people will be elected to the committee.
Also, there must be equal number of men and women which means that there must be n/2 men and n/2 women.

So out of n men, n/2 should be selected
and out of n women, n/2 should be selected.

Total ways of doing that

nC(n-2) x nC(n-2)
=
n!^2
----------
(n/2)!^4

very good.

...and this isn't even the complete answer to the question, unless you make an unwarranted assumption. namely, this is the correct answer to the question only if the committee is chosen from the employees that have already been recommended by the regional offices.
to solve the problem as it's literally written, we'd have to know the number of employees who work at each regional office, because the different selections of men and women who could be recommended in the first place would certainly affect the total number of "different committees that could be formed".
we don't have those numbers, so apparently we're supposed to make the assumption that the recommendations have already been made.

and rr is right; there is NO WAY that this is an official gmatprep problem. in fact, any source putting forward questions like this for actual preparation (as opposed to, say, enrichment) is of little value.
what's the actual source of this problem? if you don't say, we'll have to delete the thread.

[shaji]

"in fact, any source putting forward questions like this for actual preparation (as opposed to, say, enrichment) is of little value.
what's the actual source of this problem? if you don't say, we'll have to delete the thread."

As far as I remember,this problem has featured as a Weekly Challenge problem from your company, during the olden days.

The guest who had posted the proble has not placed the answer choices.

Nevertheless, the reasonings in this thread are erroneous but offcourse stimulating!!! Please retrive this problem with the answer choices and I shall be happy to explain this matterto the full.