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  4. 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

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Q. 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

Permutations and Combinations

Solution:

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boys can be arranged in 2 ways and girls can be arranged in 2 ways. boys will be together and girls will be together.
$\therefore \quad$ total number of ways $=2 \times 2=4$ ways