Question Detail
Question
There are 10 non-collinear points in a plane. By joining them, how many triangles can be made?
Correct Answer
Option D is the correct answer.
Detailed Explanation
A triangle is formed by joining any three non-collinear points. Since the points are given as non-collinear, any set of three points will form a triangle. The order in which the three points are chosen does not matter. Therefore, this is a combination problem. We need to choose 3 points out of 10. The formula for combinations is C(n, r) = n! / (r! * (n-r)!). Here, n=10 and r=3. So, C(10, 3) = (10 * 9 * 8) / (3 * 2 * 1) = 10 * 3 * 4 = 120 triangles.
Hint
A triangle is formed by selecting three points, and the order of selection does not affect the triangle formed.