In how many way can a game of tennis be played from 3 men and 4 women when each team contains one man and one woman: (a) 72 (b) 36 (c) 42(d) 144​

We should first select first playing side for the tennis game. So, we select one lady and one gentleman for this game and thus the number of this side is (4c1)∗(3C1) For the other side of the team (3C1)∗(2C1) Let us assume that we have ladies named A,B,C and D and Gents E,F and G. In my above argument I am assuming that A and E playing as team 1 against B and f playing as team 2 is a different case when A and E are playing as team 2 against B and F playing as team 1. That is, I have created a distinction between team 1 and 2. and Since, only the teams matter not their team no. I simply divide the result by 2. Thus the answer is 72/2=36