With how many ways can there be $n$ couplings between $n$ men and $n$ women?

Question

Could you help me with the following exercise? Could you give me a hint?

With how many ways can there be $n$ couplings between $n$ men and $n$ women?

Answer 1

Start with a woman(ladies first)... how many men has she to choose from? Then with another woman... $$n(n-1)...$$