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

  • question_answer
    Ravish writes letters to his five friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?

    A) 109

    B) 118

    C) 119

    D) None of these

    Correct Answer: C

    Solution :

    [c] Required number of ways \[\sum\limits_{r=2}^{5}{^{5}{{C}_{5-r}}D(r)}\] \[=\sum\limits_{r=2}^{5}{\frac{5!}{r!(5-r)!}r!\left\{ 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+...+\frac{{{(-1)}^{r}}}{r!} \right\}}\] \[=10+20+(60-20+5)+(60-20+5-1)\] \[=10+20+45+44=119\]

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