Question

How many triangles can be formed by joining four points on a circle?

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is A

$4$

Explanation for the option:

Step 1. Formula for Combination

${\mathit{n}}_{{\mathbf{c}}_{\mathbf{r}}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}$
Here, $n=4\&r=3$

Step 2.Finding how many triangles can be formed:

Because out of $4$ point only $3$ point needed to make triangle.

$\begin{array}{rcl}{4}_{c_3}& =& \frac{4!}{3!(4-3)!}\\ & =& \frac{4\times 3\times 2\times 1}{3\times 2\times 1\times \left(1\right)!}\\ & =& 4\end{array}$

Hence correct option is $\left(A\right)$