Question

How many triangles can be formed by using 7 non-collinear points on a plane?

• A. 30
• B. 35
• C. 40
• D. 50

Hint:

Use the combination formula nC3 to select 3 points from n non-collinear points.

Answer 1

The Correct Option is B

Step 1: Formula for the number of triangles 

The number of triangles that can be formed using n non-collinear points is given by:

\[ \binom{n}{3} = \frac{n!}{3!(n - 3)!} \]

Step 2: Apply n = 7

\[ \binom{7}{3} = \frac{7!}{3!(4!)} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35 \]

Final Answer

35 triangles