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Chapter 11: Problem 53

There are six employees in the stock room at an appliance retail store. The manager will choose three of them to deliver a refrigerator. How many three- person groups are possible?

Short Answer

Expert verified
The number of possible three-person groups is 20.

Step by step solution

01

Identify the values of n and k

In this problem, the total number of employees is 6 which is our \(n\), and the number of employees to choose is 3 which is our \(k\). So, \(n = 6\) and \(k = 3\).
02

Apply the combination formula

The formula for the combination is \(C(n, k) = \frac{n!}{k!(n-k)!}\). Plug in the values of \(n\) and \(k\) into the formula: \(C(6, 3) = \frac{6!}{3!(6-3)!}\).
03

Simplify the equation

First, calculate the factorial: \(6! = 6 脳 5 脳 4 脳 3 脳 2 脳 1\) = 720, \(3! = 3 脳 2 脳 1\) = 6. So, \(C(6, 3) = \frac{720}{6 脳 (6-3)!}\). Next, find the factorial of (6-3) which is \(3! = 6\). So, the combination becomes \(C(6, 3) = \frac{720}{6 脳 6}\).
04

Find the final answer

Finally, simplify the fraction to find the answer: \(C(6, 3) = \frac{720}{36} = 20\).

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