The number of ways of dividing 15 men and 15 women into 15 couples, each consisting of a man and a woman, is

The number of ways of choosing first couple is  15C1 15C1=152. The number of ways of choosing 2nd couple is  14C1 14C1=142, and so on. Thus, the number of ways of choosing the couples is152+142+132+…+22+12=15×(15+1)[2(15)+1]6=1240