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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.

[Hint: Number of straight lines =^{18}C_2 -^5C_2 + 1  ]

Answers (1)

Number of straight lines formed by joining 18 points taking 2 at a time= 18C_2

Number of straight lines formed by joining 5 collinear points taking 2 at a time=5C_2

5 collinear points when joined pairwise give only one line.  

Required number of straight lines= 18C_2-5C_2+1=153-10+1=144

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