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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    A person writes letters to six friends and be the number of ways so that at least two of the number of ways so that all the letters are in wrong envelopes. Then \[\operatorname{x} - y =\]

    A) 719

    B) 265

    C) 454

    D) None

    Correct Answer: C

    Solution :

    [c] If all the letters are not in the right envelopes, then at least two letters must be in wrong envelopes. \[\therefore \,\,\,x=6!-1=719.\] Now y = number of ways so that all the letters are in wrong envelopes \[=6!\left\{ 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+\frac{1}{6!} \right\}\] [Derangement formula] \[=360-120+30-6+1=265\] \[\therefore x-y=454\]


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