Practice | Hashtable

1. There are 7 non-collinear points. How many triangles can be drawn by joining these points?

A. 35

B. 10

C. 8

D. 7

Solution:

A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points.
The number of triangles formed,

\begin{aligned} =^{7} C_{3} \\ = \frac{7 \times (7 - 1) \times (7 - 2)}{3!} \\ = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} \\ = 7 \times 5 \\ = 35 \end{aligned}

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