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Chapter 10: Problem 61

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?

Short Answer

Expert verified
After performing the calculations, it is found that there are 1140 ways a group of three members can be selected to attend the conference from a club of 20 people.

Step by step solution

01

Identify the Variables

In this case, the total number of items (\(n\)) is 20 (the number of people in the club), and the number of items to choose (\(k\)) is 3 (the number of members to be selected to attend the conference).
02

Apply the Combination Formula

Plug the variables into the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), which leads to \[C(20, 3) = \frac{20!}{3!(20-3)!}\].
03

Calculate the Combination

Now calculate the factorial for each of the parts in the formula: \(20!\), \(3!\), and \((20-3)! = 17!\). Then, perform the division as indicated by the formula.

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