Question

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

Answer 1

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 6P3.

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

Answer 2

Step-by-step explanation:

Initially we shall arrange 5 girls.We can do that in 5! = 120 ways.

On arranging 5 girls we get 4 places between them, 1 at the beginning and 1 at the end i.e., we have 6 places in total.

We can arrange 3 boys in 6 places in 6p3ways = 120 ways

Total number of ways = 120*120 = 14400 ways