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Question
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point
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Solution
Total number of points = 18
Out of 18 numbers, 5 are collinear and we get a straight line by joining any two points.
∴ Total number of straight-line formed by joining 2 points out of 18 points = 18C2.
Number of straight lines formed by joining 2 points out of 5 points = 5C2
But 5 points are collinear and we get only one line when they are joined pairwise.
So, the required number of straight lines are
= 18C2 – 5C2 + 1
= `(18 * 17)/(2*1) - (5*4)/(2*1) + 1`
= 153 – 10 + 1
= 144
Hence, the total number of straight lines = 144.T
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