Answer to Question #213819 in Discrete Mathematics for Chaoudhary

Question

1. A debating team consists of three boys and two girls. Find the number n of ways they can sit in a row if the boys and girls are each to sit together.

Answer 1

• Counting the number of ways to put 3 boys and 2girls together in any order and then putting these combinations together yields the number of ways to put 3 boys and 2 girls together in any order.

The number of ways to arrange 3 boys in order from 3 options is

$P_3=3!=6$

The number of ways to arrange 2 girls in order from 2 options is

$P_2=2!=2$

There are two methods to arrange the boy and female sets.

The total number of possible combinations is

$2^{\ast }P_3\:^{\ast }P_2=2^{\ast }6^{\ast }2=24\:$

$n=24$