Question

用下图中的三个点作为顶点，可以画出多少个不同的三角形？

How many distinct triangles can be drawn using three of the dots below as vertices?

$9$

$12$

$18$

$20$

$24$

任取 $3$ 个点通常会形成三角形，只有 $2$ 组三点共线的情况除外。

选择三个点有 $\binom{6}{3} = 20$ 种方式，减去 $2$ 得到 $20 - 2 = 18$ 。

所以正确答案是 C。

Notice that choosing any of these $3$ dots forms a triangle, except for the $2$ triples that form a straight line.

There are $\binom{6}{3} = 20$ ways to choose the points, and then we subtract $2$ to get $20 - 2 = 18.$

Thus, C is the correct answer.