Q9 of 195 Page 16

Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.

6 men can be arranged in (6-1)! = 5! ways to dine at a round table.


Now, if we place 5 women in 6 empty seats between them so that no two women will be together, and this can be done in 6P5 ways i.e. in



As, the operations are dependent, so, the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.


=5!×6!


The discussion can be shown pictorially as:



[X = 6 empty seats between the 6 men(M)]


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Note: The corrected question may be as follows:


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