JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    The greatest common divisor of \[^{20}{{C}_{1}}{{,}^{20}}{{C}_{3}},...{{,}^{20}}{{C}_{19}}\] is

    A) 20

    B) 4

    C) 5

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[^{20}{{C}_{1}}{{=}^{20}}{{C}_{19}}=20\] \[^{20}{{C}_{3}}={{\,}^{20}}{{C}_{17}}=20\times 19\times 3\] \[^{20}{{C}_{5}}{{=}^{20}}{{C}_{15}}=19\times 17\times 16\times 3\] \[^{20}{{C}_{7}}{{=}^{20}}{{C}_{13}}=19\times 17\times 16\times 15\] \[^{20}{{C}_{9}}{{=}^{20}}{{C}_{11}}=19\times 17\times 13\times 11\times 5\times 8\] Clearly G.C.D. = 4

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