SATHEE: Permutations And Combinations Question 22

Permutations And Combinations Question 22

Question: The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth player just one card, is [IIT 1979]

Options:

A) $\frac{52!}{(17!)^3 3!}$

B) $ 52\ ! $

C) $ \frac{52\ !}{17\ !} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

For the first set number of ways $ ^{52}C _{17} $ . Now out of 35 cards left 17 cards can be put for second in $ ^{35}C _{17} $ ways similarly for 3rd in $ ^{18}C _{17} $ . One card for the last set can be put in only one way. Therefore the required number of ways for the proper distribution $ =\frac{52!}{35!17!}\times \frac{35!}{18!17!}\times \frac{18!}{17!1!}\times 1!=\frac{52!}{{{(17!)}^{3}}} $ .

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Permutations And Combinations Question 22

Question: The number of ways of dividing 52 cards amongst four players so that three players have 17 cards each and the fourth player just one card, is [IIT 1979]

Options:

Answer:

Solution:

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