lleegandy lleegandy

12-04-2019
Mathematics

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In the game War, players divide the 52-card deck into two smaller 26-card decks. How many 26-card "sub-decks" can be made? (Leave answer in factorial form.)

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LammettHash LammettHash

12-04-2019

There are [tex]\dfrac{52!}{(52-26)!}=\dfrac{52!}{26!}[/tex] ways of permuting 26 cards from the original deck (i.e. this number of ways to get specifically-ordered 26-card decks). Divide this number by 26! to remove duplicate arrangements, so that the number is [tex]\dfrac{52!}{(26!)^2[/tex].

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