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

  • question_answer
    Consider n points in a plane no three of which are collinear and the ratio of number of hexagon and octagon that can be formed from these n points is 4:13 then find the value of n.

    A) 14

    B) 20

    C) 28

    D) None of these

    Correct Answer: B

    Solution :

    [b] From n points number of hexagon is \[^{n}{{C}_{6}}=\frac{n!}{\{(n-6)!\}\{6!\}}\] From n points numbers of octagons is \[^{n}{{C}_{8}}=\frac{n!}{\{(n-8)!\}\{8!\}}\] Ratio of number of hexagon to number of octagon is \[\frac{\{(n-8)!\}\{8!\}}{\{(n-6)!\}\{6!\}}=\frac{7\times 8}{(n-7)(n-6)}=\frac{4}{13}\] On solving this quadratic equation we will get \[n=20\]

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