In how many different ways can 5 men and 3 women be seated in a row such that no two women are next to each other?
No two women would be seated next to each other if they sit between men. So, first the men can be arranged in 5! ways. There are six spots between the men. Number of ways to arrange the 3 women in those six spots is $$ P_6^3 $$ ways. So, total number of ways = 120*120 = 14400 ways.
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