Combinations Problem - Arranging 2n People in n Rooms with exactly 2 people in each room.

Question

In how many ways 2n people can be arranged in n rooms with exactly 2 people in each room

for example: arranging 4 people (1,2,3,4) in 2 rooms with above condition 1 is

(1,2) (3,4)

(1,3) (2,4)

(1,4) (2,3)

Thus 3 possible ways