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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. The number of such arrangements possible is

A
4
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B
6
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C
8
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D
None of these
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Solution

The correct option is A 4
As shown in figure 1,2 and X are the three boys and 3,4 and Y are three girls, Boy X will have neighbors as boys 1 and 2 and the girls Y will have neighbors as girls 3 and 4.
1 and 2 can be arranged in P(2,2) ways =2!=2×1=2 ways.
Also, 3 and 4 can be arranged in P(2,2) ways =2!=2×1=2
Hence required number of permutations =2×2=4

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