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

Explanation

In order that no two girls are together , we must arrange the 5 boys, each denoted by B, as under:
X B X B X B X B X B X
Here, B denotes the position of a boy and X that of a girl.
Number of ways in which 5 boys can be arranged at 5 places
`=""^(5)P_(5)=5! =(5xx4xx3xx2xx1)=120.`
Number of ways in which 3 girls can be arranged at 6 places (each marked X) `=""^(6)P_(3)=(6xx5xx4)=120.`
Hence, by the fundamental principle of multiplication, the required number of ways `=(120xx120)=14400.