Solve the problem.
-How many distinct triangles are determined by 7 points lying on a circle, where the vertices of each triangle are chosen from the 7 points ?
A) 210
B) 35
C) 21
D) 840

Question

Quizplus · Accepted Answer

To determine a triangle, we need to choose 3 points out of the 7. 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 points and $k$ is the number of points to choose. Here, $n=7$ and $k=3$, so the calculation is $C(7, 3) = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$.

Solve the Problem. -How Many Distinct Triangles Are Determined by 7 Points Lying