# Out of 18 Points in a Plane, No Three Are in the Same Straight Line Except Five Points Which Are Collinear. How Many (I) Straight Lines - Mathematics

Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines

#### Solution

Number of straight lines formed joining the 18 points, taking 2 points at a time = ${}^{18} C_2 = \frac{18}{2} \times \frac{17}{1} = 153$

But, when 5 collinear points are joined pair wise, they give only one line.
∴ Required number of straight lines =$153 - 10 + 1 = 144$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 33.1 | Page 17