5 men and 4 women are given playing cards. The men each get a different numbered

Question

5 men and 4 women are given playing cards. The men each get a different numbered card but they are all spades (2 of spades, 3 of spades, 4 of spades, etc.). The women each get a different numbered card but they are all diamonds (6 of diamonds, 7 of diamonds, 8 of diamonds, etc.). They put all 9 cards face down and mix them up. Each man and women chooses a card. In how many ways can every man get a spades card (doesn't have to be his original number) and every woman get a diamond card (this can not be her original number!).

Explanation / Answer

There are 5 spades cards and 4 diamonds cards. 5 mens can select 5 spades is 5! ways and 4 women can select 4 diamond in 4! ways so possible number of ways every man get a spades card and every woman get a diamond card is

5! * 4! = 2880

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