nahid078 wrote: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

Here's one approach:

First, select 2 men. These two men will be on opposite teams.
Since the order of the selected men does not matter, we can use combinations.
We can select 2 men from 4 men in 4C2 ways (6 ways)

Aside: If anyone is interested, we have a free video on calculating combinations (like 4C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Here comes the brute force part.
For every selection of 2 men, determine the number of possible games that can be played.
Let's say the 4 couples are Aa, Bb, Cc, and Dc (where the upper case letter is the husband and the lower case letter is the wife)
So, let's say we picked A and B as the two men.
The possible teams are:
- Ab versus Ba
- Ab versus Bc
- Ab versus Bd
- Ac versus Ba
- Ac versus Bd
- Ad versus Ba
- Ad versus Bc
So, when we picked A and B as the two men, there are 7 possible games to be played.

Since there are 6 different ways to choose the 2 men, the total number of possible games = (6)(7) = [spoiler]42 = D[/spoiler]

Cheers,
Brent