JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of combinations, Conditional combinations, Division into groups, Derangements

  • question_answer
    If \[^{n+1}{{C}_{3}}=2{{\,}^{n}}{{C}_{2}},\] then n = [MP PET 2000; Pb. CET 2002]

    A) 3

    B) 4

    C) 5

    D) 6

    Correct Answer: C

    Solution :

    \[^{n+1}{{C}_{3}}=2\,.{{\,}^{n}}{{C}_{2}}\] Þ \[\frac{(n+1)!}{3!\,.\,(n-2)!}=2\,.\,\frac{n!}{2!.(n-2)!}\] Þ \[\frac{n+1}{3\,.\,2!}=\frac{2}{2!}\] Þ \[n+1=6\,\,\Rightarrow \,n=5\].


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