Q102 / 180 · COMEDK 2024 (Memory Based) · Mathematics
Out of 10 given point, 3 are collinear. How many different straight line can be drawn by joining any 2 points from those 10 points?
- A40
- B36
- C42
- Correct answerD43
Solution
If there are $m$ points in which $n$ points are collinear $(m \geq n)$ then number of different straight line are ${ }^m C_2-{ }^n C_2+1$
$\Rightarrow{ }^{10} C_2-{ }^3 C_2+1=\frac{10 \times 9}{2}-3+1=45-3+1=43$
$\Rightarrow{ }^{10} C_2-{ }^3 C_2+1=\frac{10 \times 9}{2}-3+1=45-3+1=43$
Hence, the correct answer is option: 'D'.