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

  • question_answer
    If  \[{}^{n}{{P}_{4}}\ :\ {}^{n}{{P}_{5}}=1:2\], then \[n=\] [MP PET 1987; RPET 1996]

    A) 4

    B) 5

    C) 6

    D) 7

    Correct Answer: C

    Solution :

    \[\frac{n\ !}{(n-4)\ !}\times \frac{(n-5)\ !}{n\ !}=\frac{1}{2}\Rightarrow n-4=2\Rightarrow n=6\].


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