Answer:
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
