Q. 6

# Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together.

7 men can be arranged in (7-1)! = 6! ways to sit on a round table.

Now, we can place 7 women in 7 empty seats between them so that no two women will be together, and this can be done in 7! ways.

As, the operations are dependent, so, the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together =6! ×7!

The discussion can be shown pictorially as:

[W = seats between the 7 men(M)]

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