discrete math question for ratio

Question

From n men and n women one wants to select k male and k female candidates, to create either a committee or a ballot. In a ballot the members are fully ranked (first, second, ...); in a committee they remain unranked. Let Bk be the number of possible ballots and Ck - the number of possible committees. Find the ratio Bk/Ck.

(k!)2 or (2k)! or k out of 2k?

Answer 1

Hint: Do you know how many ways to choose $k$ men out of $n$ candidates, ordered and unordered? Now you have to combine that with a selection of women.

Answer 2

oh, so (2k)! would be the answer, as men and women selection process is the same. thank you so much for the detailed explanation.

Am i correct?