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Question
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
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Solution
Since no two men be together they have to be placed between
8 women and before and after the women.
w | w | w | w | w | w | w | w
There are 9 places so the 6 men can be arranged in the 9 places in 9P6 ways.
After this arrangement, the 8 women can be arranged in 8! ways.
∴ Total number of arrangements = (9P6) × 8!
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