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Out of 18 points in as plane, no three p...

Out of 18 points in as plane, no three points are in the same straight line except five points which are collinear. The number of straight lines formed by joining them is

A

144

B

153

C

152

D

140

Text Solution

Verified by Experts

The correct Answer is:
A
Total number of points = 18
Out of which 5 points are collinear, we get a straight line by joining any two points.
`therefore" "` Number of straight line formed by joining the 18 points taking 2 at a time = `""^(18)C_(2)`
and number of straight line formed by joining the 18 points taking 2 at a time `= ""^(5)C_(2)`
But 5 collinear points, when joined pairwise give only one line.
`therefore" "` Required number of straight line `= ""^(18)C_(2) - ""^(5)C_(2) + 1`
`= 153 - 10 + 1 = 144`
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