Question

The number of ways in which 5 boys and 5 girls can be seated for a photograph, so that no two girls sit next to each other is :

• A. $6!\cdot 5!$
• B. $(5!{)}^2$
• C. $\frac{10!}{(5!)}$
• D. $\frac{10!}{(5!{)}^2}$

Answer 1

Answer: (A)

$6!\cdot 5!$

Boys will arrange themselves in $5!$ Ways _B1_B2_B3_B4_B5_

And places left will be occupied by girls in ${}^6{\text{P}}_5$ Ways

$5!{\times }^6{\text{P}}_5=5!\times 6!$

$5!{\times }^6{\text{P}}_5=720$

The answer will be option A