# There are 10 points in a place, no three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?

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NDA (Held On: 21 Apr 2019) Maths Previous Year paper
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1. 90
2. 45
3. 40
4. 30

Option 2 : 45
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Electric charges and coulomb's law (Basic)
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10 Questions 10 Marks 10 Mins

## Detailed Solution

Concept

If there are n points in a plane and no three points lie on a straight line, then the total number of straight line segments that can be formed is given by: $$C\left( {n,\;2} \right) = \frac{{{\rm{n}}!}}{{2!\left( {{\rm{n\;}} - {\rm{\;}}2} \right)!}}$$

Calculation

Given: n = 10.

$$\Rightarrow \;C\left( {10,\;2} \right) = \frac{{10!}}{{2!\left( {10 - {\rm{\;}}2} \right)!}} = \frac{{10 \times 9}}{2} = 45$$

Hence, the number of straight lines that can be formed is 45.
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