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
calculates the number of ways to choose r items from a set of n items without regard to their order. It is defined as:
^nC_r = \frac{n!}{ r!(n - r)!}where “!” represents the factorial function. The factorial of a number is the product of all positive integers less than or equal to that number.
To calculate the number of triangles that can be drawn from 6 points using the combination formula, we need to choose 3 points out of the 6 available points.
Using the combination formula (nCr), we can calculate this as:
^6C_3 = \frac{6!}{ 3!(6 - 3)!}
= (6 * 5 * 4 * 3!) / (3! * 3 * 2 * 1)
= (6 * 5 * 4) / (3 * 2 * 1)
= 20
Therefore, there are 20 distinct triangles that can be drawn using any three points from the given 6 points.
The correct answer is 20.