10 10 points

Probability Level 1

In a field there are 10 10 points. Each point is connected to another point with a line. If no 3 3 points are collinear, how many possible number of triangles can we construct using the 3 dots as its vertices?


The answer is 120.

Wildan Bagus Wicaksono by Wildan Bagus Wicaksono , 18, Indonesia

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1 solution

Given 10 dots. Each triangle has 3 vertices. So the number of possible triangles is

C 3 10 = 10 ! 3 ! 7 ! = 10 ⋅ 9 ⋅ 8 3 ⋅ 2 ⋅ 1 = 120 { C }_{ 3 }^{ 10 }=\frac { 10! }{ 3!7! } =\frac { 10\cdot 9\cdot 8 }{ 3\cdot 2\cdot 1 } =120 .

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