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There Are 10 Points in a Plane of Which 4 Are Collinear. How Many Different Straight Lines Can Be Drawn by Joining These Points.

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Question

There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.

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Solution

Number of straight lines formed joining the 10 points, taking 2 points at a time = 

\[{}^{10} C_2 = \frac{10}{2} \times \frac{9}{1} = 45\]
Number of straight lines formed joining the 4 points, taking 2 points at a time =\[{}^4 C_2 = \frac{4}{2} \times \frac{3}{1} = 6\]
But, when 4 collinear points are joined pair wise, they give only one line.
∴ Required number of straight lines =\[45 - 6 + 1 = 40\]
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Chapter 17: Combinations - Exercise 17.2 [Page 16]

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R.D. Sharma Mathematics [English] Class 11
Chapter 17 Combinations
Exercise 17.2 | Q 14 | Page 16

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