A probability problem by Chung Kevin

Probability Level 3

Using these 9 points as vertices, how many triangles can be formed?

Note: Non-degenerate triangles do not count. Triangles which have the same set of 3 vertices are identical.

80 78 84 76

Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

Anthony Holm
Apr 11, 2017

Any three non-colinear points make a triangle. There are 9C3=84 ways to select 3 points and 8 of those are lines (3 lines across, 3 up and down, the 2 long diagonals), menaing the total number of triangles is 84-8=76.

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Hana Wehbi
Apr 10, 2017

I solved it by counting. Since two points connect a side, thus, 2 3 = 8 × 9 = 72 2^3 =8 \times 9 = 72 small triangles, plus the 4 4 big triangles of the sides. The answer is 76 76 .

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