There are 6 men and 5 women. They form pairs to play badminton. How many ways are there to form male-female pairs?

1. Problem Description

There are 6 men and 5 women. They form pairs to play badminton. How many ways are there to form male-female pairs?

2. Solution Steps

We need to find the number of ways to match each of the 5 women with one of the 6 men.

The first woman has 6 choices of men to pair with.

The second woman also has 6 choices of men to pair with.

The third woman also has 6 choices of men to pair with.

The fourth woman also has 6 choices of men to pair with.

The fifth woman also has 6 choices of men to pair with.

However, the problem likely implies each woman is paired with a different man.

In this case,

The first woman can choose from 6 men.

The second woman can choose from the remaining 5 men.

The third woman can choose from the remaining 4 men.

The fourth woman can choose from the remaining 3 men.

The fifth woman can choose from the remaining 2 men.

The total number of ways is $6 \times 5 \times 4 \times 3 \times 2$.

$6 \times 5 \times 4 \times 3 \times 2 = 30 \times 12 \times 2 = 30 \times 24 = 720$

3. Final Answer

720