Question

In how many different ways can $5$ boys and $5$ girls form a circle such that the boys and girls are alternate?

• A. $2880$
• B. $2440$
• C. $2536$
• D. $4125$

Answer 1

The correct option is A $2880$

First let us place the boys. There are $5$ boys and they can be seated in $(5-1)!=4!=24$ ways.

$\Rightarrow$ Now there are $5$ gaps in which the $5$ girls are to be seated $={}^5{P}_5=5!=120$

$\Rightarrow$ Total $=24\times 120=2880.$

Hence, the answer is $2880.$