JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Geometrical Problems

  • question_answer
    The number of straight lines that can be formed by joining 20 points no three of which are in the same straight line except 4 of them which are in the same line [Kerala (Engg.) 2002]

    A) 183

    B) 186

    C) 197

    D) 185

    Correct Answer: D

    Solution :

      Required number \[={{\,}^{20}}{{C}_{2}}\,-{{\,}^{4}}{{C}_{2}}\,+\,1\] \[=\frac{20\times 19}{2}-\frac{4\times 3}{2}+1=190-6+1=185.\]


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