(i) In how many ways can 6 boys and 4 girls be seated in a round table

1.	(i) In how many ways can 6 boys and 4 girls be seated in a round tableso that two girls never be seated together.
Answer» Let us treat two girls as a single entity(for sake of ‘togetherness’) Now these two girls can be selected from 4 girls in 4c2 ways. Now,total no of members =6 boys+3 girls (2 girls has been counted as one). We know that n members can be seated in a circle in (n-1)! Ways. So 9 members can be seated in 8! Ways. And the two girls who were treated as one could exchange their position in 2! Ways. So total no of ways so that 2 girls be seated together= [(8!×2!×4c2)] So,required answer is 9!-(8!×2!×4c2)

(i) In how many ways can 6 boys and 4 girls be seated in a round tableso that two girls never be seated together.

Answer»

Let us treat two girls as a single entity(for sake of ‘togetherness’)

Now these two girls can be selected from 4 girls in 4c2 ways.

Now,total no of members =6 boys+3 girls (2 girls has been counted as one).

We know that n members can be seated in a circle in (n-1)! Ways.

So 9 members can be seated in 8! Ways.

And the two girls who were treated as one could exchange their position in 2! Ways.

So total no of ways so that 2 girls be seated together= [(8!×2!×4c2)]

So,required answer is 9!-(8!×2!×4c2)