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Question
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear.
Solution
To draw a line, two points are needed.
There are 10 points in a plane such that no three of them are collinear.
Hence, the number of lines formed 10C2
= `(10!)/((10 - 2)!2!)`
= `(10!)/(2!8!)`
= `(10 xx 9xx8!)/(2xx1xx8!)`
= 5 × 9
= 45
45 straight lines are obtained if no three points are collinear.
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