Answer to Question #347233 in Discrete Mathematics for Shal

Question

There are 10 girls and 7 boys in a class and need to select 4 students as a school representative. In how many ways can we select of 2 girls and 2 boys?

Answer 1

We can select 2 out of 7 boys in $\frac{7!}{2!5!}= 21$ ways.

We can select 2 out of 10 girls in $\frac{10!}{2!8!}= 45$ ways.

We can select 2 boys and 2 girls in $21\cdot 45=945$ ways.

Answer: 945 ways.