Question

the number of ways in which 6 boys and 3 girls can sitting around a round table so that all the girls come together

Answer 1

Let us assume 12 positions(1–12).

Let’s place a boy in one position and shuffle remained ones around him.

As if no two boys should sit together,there is only way for them to place all the boys is placing alternately.

Now sguffling these 5 boys (excluding initially placed one because it doesn’t matter where ever we place him) gives us 5! possibilities.

And for six girls we have 6! possibilities.

Therefore total number of ways are5!×6!

=86400.