Out of 8 points ina plane , 5 are collinear. Find the probability that 3 points selected at random will form a triangle.
Answers
Answered by
42
3 points can be chosen from 8 points in ⁸C₃=56 ways.
To form a triangle,
When one point is chosen from 5 collinear points and 2 points are chosen from remaining 3 points, this can be done in ⁵C₁.³C₂=15 ways.
When 2 points are chosen from 5 collinear points and 1 point is chosen from remaining 3 points, this can be done in ⁵C₂.³C₁=30 ways.
When all the 3 points are chosen from remaining 3 points,this can be done in ³C₃=1 ways.
∴, the required probability is
=(15+30+1)/56
=46/56
=23/28 Ans.
To form a triangle,
When one point is chosen from 5 collinear points and 2 points are chosen from remaining 3 points, this can be done in ⁵C₁.³C₂=15 ways.
When 2 points are chosen from 5 collinear points and 1 point is chosen from remaining 3 points, this can be done in ⁵C₂.³C₁=30 ways.
When all the 3 points are chosen from remaining 3 points,this can be done in ³C₃=1 ways.
∴, the required probability is
=(15+30+1)/56
=46/56
=23/28 Ans.
Answered by
2
Total number of outcomes=C3
5^C1.3^C2+5^C2.3
^C1+1
hence probability that 3 points selected will form a triangle.
5^C1.3^C2+5^C2.3
^C1+1
hence probability that 3 points selected will form a triangle.
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