JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer 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]

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

    B) \[52\ !\]

    C) \[\frac{52\ !}{17\ !}\]

    D) None of these

    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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