Question

in how many ways 5 boys and 6girls can be seated in a long bench so that each boy will sit between two girls​

Answer 1

Answer:

hey here is your answer

There are total 11 people and 12 chairs. Assume that V sits on the vacant chair. Now we have 12 chairs around a round table and 12 distinct "people".

Let's make the girls sit first.

One girl sits on any chair in 1 way (chairs around a table are not distinct relative to each other).

Now there are 11 distinct chairs (first to the girl's left, second to the girl's left, first to the girl's right etc).

Only 5 are available for the 5 girls - the chairs on either side of the girl are not available for girls. The girls can sit on only the alternate chairs. So 5 girls can sit on 5 distinct chairs in 5! ways.

Now 6 distinct chairs are leftover and 6 distinct people have to occupy them. This can be done in 6! ways.

Total number of arrangements = 1*5!*6! = 5! * 6!

hope it help you ☺️

Answer 2

total chairs=11

the boys have to sit between 2girls,

this can be only possible when the boy will sit in 9 seats, ,except first and last seat,

so permutation of boy=9P5

total no. of possibilities will, recognizeed by ,no. of ways in which boys can,sit

so total possiblties=9!/5!=9×8×7×6

3024

hope it helps you