# Out of 18 Points in a Plane, No Three Are in the Same Straight Line Except Five Points Which Are Collinear. How Many (Ii) Triangles Can Be Formed by Joining Them? - Mathematics

Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?

#### Solution

Number of triangles formed joining the 18 points, taking 3 points at a time =${}^{18} C_3 = \frac{18}{3} \times \frac{17}{2} \times \frac{16}{1} = 816$

Number of straight lines formed joining the 5 points, taking 3 points at a time =${}^5 C_3 = \frac{5}{3} \times \frac{4}{2} \times \frac{3}{1} = 10$

∴ Required number of triangles =$816 - 10 = 806$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 33.2 | Page 17