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  4. Number of ways in which 5 boys and 5 girls can be seated alternatively on a round table if a particular boys and a particular girl are never adjacent to each other in any arrangement, is

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Q. Number of ways in which 5 boys and 5 girls can be seated alternatively on a round table if a particular boys and a particular girl are never adjacent to each other in any arrangement, is

Permutations and Combinations

Solution:

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$ B_1 \mid G_1$ always separated.
5 boys can be seated in 4 ! now for $G_1$ can not sit between $B _1$ and $B _2$ or $B _1$ and $B _5$ and therefore can set only in 3 ways and the remaining 4 girls in 4 ! ways.
Total ways $(4 !)(3)(4 !)=576 \times 3=1728$