Question

peaceful travel agency offers vacation packages. each vacation package includes a city, a month, and an airline. the agency has 3 cities, 1 month, and 2 airlines to choose from. how many different vacation packages do they offer?

Explanation:

Step1: Apply the counting principle

The counting principle states that if there are \(m\) ways to do one thing, \(n\) ways to do a second thing, and \(p\) ways to do a third thing, then the total number of ways to do all three things together is \(m\times n\times p\). Here, the number of choices for cities \(m = 3\), for months \(n = 1\), and for airlines \(p = 2\).

Step2: Calculate the total number of packages

Using the formula from the counting principle, we calculate \(3\times1\times2\). First, \(3\times1 = 3\), then \(3\times2 = 6\).

Answer:

6