The number of ways of dividing 15  men and 15  women into 15  couples, each consisting of an 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 is   152+142+132+......+22+12     =15×(15+1)[2(15)+1]6=1240