Left hand glove and Right hand glove There are n pairs of gloves and n men. In how many ways can each of the n men have a left hand of one pair and a right hand of another pair of gloves. I thought its a simple question of derangements of n objects but I am not getting correct answer.

We assume the gloves are distinct. The left-hand gloves can be assigned in $n!$ ways. For each of these ways, the right-hand gloves can be assigned in $D_n$ ways.