The number of ways in which a mixed doubles tennis game can be arranged from 9 married couples:

Options

A. 3024
B. 1512
C. 2592
D. 6048

Answer

To solve the problem of arranging a mixed doubles tennis game from 9 married couples, we need to follow these steps:

### Step 1: Understand the Requirements
In a mixed doubles tennis game, we need to select 2 males and 2 females from the 9 married couples. Each couple consists of one male and one female.

### Step 2: Select the Males
We need to choose 2 males from the 9 husbands. The number of ways to choose 2 husbands from 9 is given by the combination formula:

\[ \text{Number of ways to choose 2 husbands} = \binom{9}{2} \]

Calculating this, we have:

\[ \binom{9}{2} = \frac{9 \times 8}{2 \times 1} = 36 \]

### Step 3: Select the Females
Similarly, we need to choose 2 females from the 9 wives. The number of ways to choose 2 wives from 9 is also given by the combination formula:

\[ \text{Number of ways to choose 2 wives} = \binom{9}{2} \]

This calculation is the same as for the husbands:

\[ \binom{9}{2} = 36 \]

### Step 4: Arrange the Selected Players
Once we have selected 2 husbands and 2 wives, we need to arrange them on the court. The arrangement can be done in different ways. Specifically, the two males can be paired with the two females in different configurations. The number of arrangements of 2 males and 2 females can be calculated using the factorial of the number of pairs:

\[ \text{Number of arrangements} = 2! = 2 \]

### Step 5: Calculate the Total Number of Ways
Now, we can calculate the total number of ways to arrange the mixed doubles game by multiplying the number of ways to choose the husbands, the number of ways to choose the wives, and the number of arrangements:

\[ \text{Total ways} = \binom{9}{2} \times \binom{9}{2} \times 2! \]

Substituting the values we calculated:

\[ \text{Total ways} = 36 \times 36 \times 2 = 2592 \]

### Final Answer
The total number of ways in which a mixed doubles tennis game can be arranged from 9 married couples is **2592**.

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