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

  • question_answer
    The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is [Roorkee 1989; BIT 1989; MP PET 1995;Pb. CET 1997, 98; Roorkee 2000; DCE 2002; AMU 2005]

    A) 185

    B) 175

    C) 115

    D) 105

    Correct Answer: A

    Solution :

    Required number of ways \[={{\,}^{12}}{{C}_{3}}{{-}^{7}}{{C}_{3}}\]               \[=220-35=185\].


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