A mixed doubles tennis game is to be played between two teams. There are four married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played? A. 12

B. 21

C. 36

D. 42

E. 46

42 games.

Step-by-step explanation:

To start you have to select 2 women who will be in opposite teams. In this case, the order of women does NOT matter, therefore combinations are used. Then the combination would be as follows:

Select 2 women from 4 women in 4C2 (6 ways)

Now, for each selection of 2 women, you have to determine the number of possible games that can be played.

Assuming that the 4 couples are Ww, Xx, Yy and Zz (where the uppercase letter is the wife and the lowercase letter is the husband)

So, let's say we choose W and X as the two women.

Possible teams are:

- Wx vs Xw

- Wx vs Wy

- Wx vs Xz

- Wy vs Xw

- Wy vs Xz

- Wz vs Xw

- Wz vs Xy

So, when we choose W and X as the two women, there are 7 possible games to play.

As there are 6 different ways to choose the 2 women, the total number of possible games = (6) * (7) = 42