Answer to Question #161788 in Discrete Mathematics for afzal

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

The number of ways of placing 3 boys together and 2 girls together in any order may be obtained by counting the number of ways of placing the three boys together and two girls together and then placing these combinations together.

The number of ways of placing 3 boys in order out of 3 selections is:

P₃ = 3!= 6

The number of ways of placing 2 girls in order out of 2 selections is:

P₂ = 2!= 2

There are two ways of placing the sets of boys and girls.

The total number of ways of placing them together is:

2*P₃*P₂=2*6*2=24

Answer: n = 24