Problem 61 - College Algebra

Question

Solve by the method of your choice. From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?

Step-by-Step Solution

Answer

The group of three members can be selected in 1140 different ways.

Step 1: Identify values for \(n\) and \(k\)

In this problem, the total number of people, \(n\), is 20. The number of people to choose, \(k\), is 3.

Step 2: Substitute the values into the formula

Substitute these values into the combination formula: \( C(n, k) = \dfrac{20!}{3!(20-3)!} \) = \( \dfrac{20!}{3! \cdot 17!} \)

Step 3: Simplify the expression

First calculate the factorial for these numbers \(20!\), \(3!\) and \(17!\) . Then substitute the obtained values into the combination equation and simplify.

Step 4: Simplify the equation

Simplify the equation to obtain the answer.