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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 neighbor and the girl Y does not want any boy neighbor. The number of such arrangements possible is

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None of these

answer is A.

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Detailed Solution

Total boys = 3 boys such that,
B1, B2, and X
Also the total girls = 3 girls such that,
G1, G2 and Y
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Here, X boy does not want any girl neighbor.
So, x will sit between 2 boys which is B1, B2.
So, total ways in which B1 and B2 boys can be arranged themselves,

= 2!

= 2

Also, Y does not want to sit near boy. So, she will sit between G1 and G2.
Here, number of ways in which girls G1and G2can arrange themselves,

= 2!

= 2

So, the required ways,

= 2! \times 2!

= 4

Correct option is 1.

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