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

  • question_answer
    If  \[^{n}{{P}_{5}}=9{{\times }^{n-1}}{{P}_{4}}\],  then the value of \[n\] is

    A) 6

    B) 8

    C) 5

    D) 9

    Correct Answer: D

    Solution :

    \[\frac{^{n}{{P}_{5}}}{^{n-1}{{P}_{4}}}=9\Rightarrow \frac{n\,!}{(n-5)\,!}\times \frac{(n-5)\,!}{(n-1)\,!}=9\Rightarrow n=9\].

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