Question

Three boys and three girls are to be seated around a round table in a circle.

Among them the boy $X$ does not want any girl neighbor and the girl $Y$ does not want any boy neighbor then the number of such arrangements is ?

• A. $2$
• B. $4$
• C. $2^3$
• D. $3^3$

Answer 1

The correct option is B

$4$

Explanation of the correct option.

Step $1$: Find neighbors of $X$ and $Y$.

Let's draw a circular table and place $X$ and $Y$ accordingly.

In the figure, $1,2$ and $X$ are the three boys and $3,4$ and $Y$ are the three girls.

Boy $X$ will have neighbor as boys $1,2$, other side $Y$ will have neighbor as girl $3,4$.

Step $2$: Find the number of ways they can be arranged.

Boys $1,2$ can arranged in ways $=2!$

$=2ways$

Other side girls $3,4$ can be arranged in ways $=2!$

$=2ways$

Therefore, total arrangements possible $=2\times 2$

$=4$

Hence option (B) is the correct option, i.e. $4$.