Question

In how many ways 8 boys and 5 girls can sit around a round table, so that no two girls sit together.

• A. $\frac{7!}{3!}$
• B. $8\left(\frac{7!}{3!}\right)$
• C. $\frac{(7!{)}^2}{3!}$
• D. $8\left[\frac{(7!{)}^2}{3!}\right]$

Answer 1

The correct option is D $8\left[\frac{(7!{)}^2}{3!}\right]$

8 boys can be seated in a round table in 7! Ways.
There are 8 spaces between the boys, which can be occupied by 5 girls in ${}^8{P}_5.$
Hence total number of ways $=7!\ast \left(\frac{8!}{3!}\right)=8\left[\frac{(7!{)}^2}{3!}\right]$