Question

in how many ways can 4 boys and 4 girls be made to sit around a circular table if no two boys sit adjacent to each other

Answer 1

Point to be noted: As it is a round table, the no.of possible ways are (n-1)! ways.

Condition is no two boys should sit adjacent to each other.
So, first arrange 4 girls in a round table such that they aren't adjacent to each other (as here, no. of boys = no.of girls)

So no.of possible ways arranging the girls in a round table = (4-1)! = 3! ways
Now, let the boys made to sit in the remaining gaps in 4! ways

Therefre total no.s of ways in which this condition is possible = 3! x 4! ways.
                                                                                                 = 6 x 24 ways
                                                                                                 = 144 ways.



Therefore, the no. of ways in which 4 boys and 4 girls can be made to sit around a circular table such that no two boys sit adjacent to each other are 144 ways.

Answer 2

Answer:

Each clockwise permutation has a matching anticlockwise ... there are 3 places for the other 3 boys that is 3! ... We have 4 ways of choosing a boy to sit ........................