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Question
Eight men and six women sit around a table. How many of sitting arrangements will have no two women together?
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Solution
8 men can be seated around a table in (8 – 1)! = 7! ways.
There are 8 gaps created by 8 men’s seats.
∴ Women can be seated in 8 gaps in 8P6 ways
∴ Total number of arrangements so that no two women are together = 7! × 8P6
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