Question

Eight men and six women sit around a table. How many of sitting arrangements will have no two women together?

Answer 1

8 men can be seated around a table in (8 − 1)! = 7! ways.
There are 8 gaps created by 8 men’s seats.
∴ 6 Women can be seated in 8 gaps in ⁸P₆ ways
∴ Total number of arrangements so that no two women are together = 7! × ⁸P₆