there are 12 points in a plane, of which 5 are collinear. Find the number of triangle that can be formed with vertices at these points and the number of straight lines obtained by joining these points in pairs
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Answered by
65
Answer:
210 Triangles
57 straight lines
Step-by-step explanation:
There are 12 points in a plane, of which 5 are collinear.
to find number of triangle that can be formed with vertices at these points
we will Divide the Triangle into 3 categories
1. Triangle with two vertices from 5 colinear points
2. Triangle with one vertices from 5 colinear points
3. Triangle with all the vertices from (12-5 = 7) points
Number of Triangle = ⁵C₂*⁷C₁ + ⁵C₁*⁷C₂ + ⁷C₃
= 10*7 + 5*21 + 35
= 70 + 105 + 35
= 210
210 Triangles
total number of straight lines with 12 Points are
=¹²C₂ = 66
but here 5 Colinear points will give only one straight line
instead of ⁵C₂ = 10
Total Number of Straight lines = 66 - 10 + 1 = 57
Answered by
5
Answer:
120 and 57
............
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