There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?

Step-by-step solution

From 10 given points, ¹⁰ C₂ straight lines can be drawn. But 4 points are collinear, using 4 points, ^4 C₂ straight lines can be drawn. From 4 collinear points, 1 straight line can be drawn. So, total number of straight lines = ¹⁰ C₂- ^4 C₂+1 aligned & = 10 ! 8 ! 2 ! - 4 ! 2 ! 2 ! +1 & =45-6+1=40 aligned