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Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if

(a) no three points are collinear

(b) four points are collinear

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There are 10 points on a plane.

(a) When no three of them are collinear. A line is obtained by joining 2 points.

∴ Number of lines passing through these points  = 10C2

(b) When 4 of them are collinear. If no three points are collinear, we get a total of 10C2 = 45 lines by joining them. …..[From (a)]

Since 4 points are collinear, only one line passes through these points instead of 4C2 lines.

∴ C – 1 extra lines are included in 45 lines.

Number of lines passing through these points

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