# Q. ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?

(a) 16

(b) 18

(c) 20

(d) 24

Correct Answer: (c) 20

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## ABCD square. Points on sides AB, CD, BC, DA.

The total number of ways to choose 3 points out of 6 is given by the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of items, r is the number of items to choose, and “!” denotes factorial.

So, the total number of triangles is C(6, 3) = 6! / [3!(6-3)!] = 20.