There are 10 points in a plane, no three of which are in the same straight line excepting 4, which are collinear. Then, number of

We know that join of any two points gives a line.The number of lines obtained from 10 points, no three of which are collinear =10C2=10×92×1=45Lines obtained from 4 points =4C2=4×32×1=6∴ Number of lines lost due to 4 collinear points= 6 – 1 = 5∴ Required number of lines = 45 – 5 = 40.Also, We know that any triangle can be obtained by joining any three points not in the same straight line.∴ Number of triangles obtained from 10 points, no three of which are collinear =10C3=10×9×83×2×1=120Triangle obtained from 4 points =4C3=4∴ Number of triangles lost due to 4 collinear points = 4.∴ Required number of triangles = 120 – 4 = 116.