Question

There are 15 points in a plane such that no three of them are collinear. The number of triangles formed by joining them is
1. 455
2. 2730
3. 355
4. 454

Answer 1

Correct Answer - Option 1 : 455

Concept:

Combination formula:

The formula of a combination of r objects out of n objects is given as follows:

\(\rm ^nC_r = \dfrac{n!}{r!(n-r)!}\)

Calculation:

There are 15 points in a plane the triangle formed by joining the three-point

Therefore,

Number of triangle = ¹⁵C₃

= \(\dfrac{15!}{3!(15-3)!}\)

= \(\dfrac{15\times14\times13}{3\times2}\)

= 455