Question:
Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them is ________.
Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them is ________.
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Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them is ____.
Updated On: Apr 15, 2026
- 143
- 144
- 153
- None of these
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Formula
Number of lines from $n$ points $= {}^nC_2$.
Step 2: Total Lines
Total lines $= {}^{18}C_2 = \frac{18 \times 17}{2} = 153$.
Step 3: Collinear Adjustment
Subtract lines formed by 5 collinear points $({}^5C_2 = 10)$ and add back 1 (since they form exactly one line).
Step 4: Calculation
$153 - 10 + 1 = 144$.
Final Answer: (B)
Number of lines from $n$ points $= {}^nC_2$.
Step 2: Total Lines
Total lines $= {}^{18}C_2 = \frac{18 \times 17}{2} = 153$.
Step 3: Collinear Adjustment
Subtract lines formed by 5 collinear points $({}^5C_2 = 10)$ and add back 1 (since they form exactly one line).
Step 4: Calculation
$153 - 10 + 1 = 144$.
Final Answer: (B)
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