Question

Three boys and three girls are to be seated around a table in a circle. Among them the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible?

• A. 5
• B. 6
• C. 4
• D. 2

Answer 1

Answer: (C)

4

Answer 2

The positions of X and Y are fixed, with the three boys grouped together around X in the center, and the three girls grouped together around Y in the center.
The number of arrangements for boys=$(3 − 1)! = 2! = 2$
Similarly for girls=$2! = 2$
$\therefore$ Total number of ways= $2\times2=4$
The correct option is (C): 4