SATHEE: Permutations And Combinations Question 347

Permutations And Combinations Question 347

Question: There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is:

Options:

A) 816

B) 806

C) 805

D) 813

Show Answer

Answer:

Correct Answer: B

Solution:

[b] A triangle can be formed by using three no collinear points. So, the number of triangles formed by 18 non-collinear points $ {{=}^{18}}C_3 $ But according to the question, 5 points are collinear. Hence, exact number of triangles $ {{=}^{18}}C_3{{-}^{5}}C_3=\frac{18!}{3!15!}-\frac{5!}{3!2!} $ $ =\frac{16\times 17\times 18}{2\times 3}-\frac{4\times 5}{2}=816-10=806. $

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Permutations And Combinations Question 347

Question: There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is:

Options:

Answer:

Solution:

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