Answer to Question #184964 in Combinatorics | Number Theory for gian

Question

Coach Tab will select 3 girls and 3 boys for

the mix volleyball games. If he has 7 girls

and 8 boys on the pool, how many different

combinations can he have?

Answer 1

$C_7^3\cdot C_8^3=\frac{7!}{3!4!}\cdot \frac{8!}{3!5!}=\frac{5•6•7•6•7•8}{6•6}=5•7•7•8=1960.$