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

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), $k$ is the number of items to choose (3 for a triangle), and $n!$ denotes the factorial of $n$. Therefore, the number of triangles that can be formed is $C(8, 3) = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$.

Solve the Problem. -Three Noncollinear Points Determine a Triangle. How Many Triangles Can