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

Answer 1

Answer: (A)

$6 \,! \,5 \,!$

Answer 2

The correct option is(A): 6!5!.

$X.X.X.X.X.$ First place $5$ boys at the $X$ places. This can be done in $5!$. Since no two girls sit next to each $\therefore$ we can give them seats at places marked by This can be done in $^{6}p_{5}$ ways. $=6\times5\times4\times3\times2=6!$ ways. $\therefore$ reqd. number of ways $= 6! \,5!$