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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  \[{}^{n}{{P}_{5}}=20.\ {}^{n}{{P}_{3}}\], then \[n=\]

    A) 4

    B) 8

    C) 6

    D) 7

    Correct Answer: B

    Solution :

      \[\frac{n\ !}{(n-5)\ !}\times \frac{(n-3)\ !}{n\ !}\]=20 \[\Rightarrow \]\[(n-3)(n-4)=20\Rightarrow n=-1,\ 8\] But \[-1\] is not exceptable.


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