Permutations And Combinations Question 349

Question: Two straight line intersect at a point O. Points $ A_1,A_2,…A _{n} $ are taken on one line and pints $ B_1,B_2,…,B _{n} $ on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is

Options:

A) $ n(n-1) $

B) $ n{{(n-1)}^{2}} $

C) $ n^{2}(n-1) $

D) $ n^{2}{{(n-1)}^{2}} $

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Answer:

Correct Answer: C

Solution:

  • [c] No. of triangles $ {{=}^{2n}}C_3{{-}^{n}}C_3{{-}^{n}}C_3 $ $ =\frac{2n(2n-1)(2n-2)}{6}-\frac{2n(n-1)(n-2)}{6} $ $ =\frac{1}{3}n(n-1)(3n)=n^{2}(n-1). $