Three noncollinear points determine a triangle. How many triangles can be formed with 8 noncollinear points?
A) 56
B) 6720
C) 336
D) 24

Question

Quizplus · Accepted Answer

To form a triangle, you need to choose any 3 points out of the 8 noncollinear points. The number of ways to do this is given by the combination formula $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items (points in this case), and $k$ is the number of items to choose (3 points for a triangle). So, $C(8, 3) = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$.

Three Noncollinear Points Determine a Triangle