In how many ways can 5girls and 3 boys be seated in a row so that no two boys are together

Here In the question, there are 5 girls. 5 girls can be seated in ⁵P₅=5x4x3x2x1=5! ways. After arranging the girls in 5 ways, boy can sit in 6 places, as given below by $ sign:

$ G $ G$ G $ G $ G $

Now, the question says that no two boys can sit togerher. So there are 6 places where these 3 boys can sit. So now the boys can sit in ⁶P_3.

Therefore, the total number of seating arrangements possible

=⁵P₅ x ⁶P₃

= 5 x 4 x 3 x 2 x 1 x 6 x 5 x 4 ways

=14400 ways