There are 10 points in a plane, no three of which are in the same straight line,excepting 4 points ,which are collinear.Find the (i)number of straight lines obtained from the pairs of these points (ii)number of triangles that can be formed with the vertices as these points..Explain with diagram
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40 lines , 116 Triangles if There are 12 points in a plane, of which 4 are collinear.
Step-by-step explanation:
Total 10 point
4 points are in same straight line
Number of Straight line
Case 1 : Both point are from 4 points - 1 Line
Case 2 : Both points are from remaining 6 points = ⁶C₂ = 15 lines
Case 3 : 1 point from 6 & 1 from 4 = ⁴C₁ * ⁶C₁ = 24 Lines
Total lines = 1 + 15 + 24 = 40
Number of triangles
1. Triangle with two vertices from 4 colinear points ⁴C₂*⁶C₁ = 36
2. Triangle with one vertices from 4 colinear points = ⁴C₁*⁶C₂ = 60
3. Triangle with all the vertices from 6 points = ⁶C₃ = 20
total triangles = 36 + 60 + 20 = 116
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