2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Permutations and Combinations

JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Multinomial Theorem, Number of Divisors, Miscellaneous problems

  • question_answer
    If \[^{n}{{P}_{4}}=24.{{\,}^{n}}{{C}_{5}},\] then the value of n is  [Karnataka CET 2001]

    A) 10

    B) 15

    C) 9

    D) 5

    Correct Answer: C

    Solution :

    Given, \[^{n}{{P}_{4}}=24\,.{{\,}^{n}}{{C}_{5}}.\]  Therefore,\[n(n-1)\,(n-2)\,(n-3)\]   \[=24\times \frac{n(n-1)\,(n-2)\,(n-3)\,(n-4)}{5.4.3.2.1}\] \[\Rightarrow \]\[1=\frac{(n-4)}{5}\]  Þ \[n-4=5\]  Þ \[n=9\].


You need to login to perform this action.
You will be redirected in 3 sec spinner