JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Mock Test - Permutations and Combinations

  • question_answer
    The number of triangles that can be formed with 10 points as vertices, n of them being collinear, is 110. Then n is

    A) 3                     

    B) 4

    C) 5        

    D) 6

    Correct Answer: C

    Solution :

    [c] Out of 10 points let n points be collinear. Then the number of triangles is \[^{10}{{C}_{3}}{{-}^{n}}{{C}_{3}}=110\] or \[\frac{10\times 9\times 8}{6}-\frac{n(n-1)(n-2)}{6}=110\] or \[n(n-1)(n-2)=60\] or \[n=5\]         

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