Find the number of ways in which 5 boys and 3 girls can be seated in a row so that no two girls are together ?

Concept:

The number of ways to arrange n distinct things taken all at a time is given by: 

Let r and n be the positive integers such that, 0 ≤ r ≤ n. Then the number of ways to arrange   r thing taken at a time out of n different things is given by: 

Calculation:

Given: There are 5 boys and 3 girls that can be seated in a row such that no two girls are together.

First let's calculate number of ways to arrange boys in the row.

∵ There are 5 boys so they will occupy 5 places in  ways = 120 ways

We can arrange the 3 girls in 6 places shown by cross mark : X B X B X B X B X B X

Number of ways in which 3 girls can seat in 6 places denoted by cross mark = 

As we know that, 

⇒ 

∴ The required number of ways = 120 × 120 = 14400