JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    In how many ways \[n\] books can be arranged in a row so that two specified books are not together

    A) \[n\,!\,-(n-2)\,!\]

    B) \[(n-1)\,!\,(n-2)\]

    C) \[n\,!-2(n-1)\]

    D) \[(n-2)\,n!\]

    Correct Answer: B

    Solution :

    Total number of arrangements of \[n\] books \[^{6}{{P}_{5}}\times 5\ !=86400\]. If two specified books always together then number of ways \[=(n-1)\ !\ \times 2\] Hence required number of ways \[=n\ !-(n-1)\ !\ \times 2\] \[=n(n-1)\ !\ -(n-1)\ \times 2=(n-1)\ !\ (n-2)\].

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