Discussion

There are 20 points in a plane, how many triangles can be formed by these points if 5 are colinear?

Answer: A

A triangle needs three points, but three collinear points give no triangle.

\[ \text{all triples} = {}^{20}C_{3} = 1140 \]

\[ \text{collinear triples} = {}^{5}C_{3} = 10 \]

\[ 1140 - 10 = 1130 \]

Only the five collinear points can produce a degenerate triple, so just one subtraction is needed.

No comment is present. Be the first to comment.

Loading…