UPSC NDA Math Model Paper 6

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 5P5 = 5! 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 =6P3
As we know that, ‌nPr=

n!

(n−r)!

⇒‌6P3=120
∴ The required number of ways =120×120=14400