Question

1. stephen has packed 8 shirts, 6 pairs of pants and 3 pairs of shoes for vacation. how many possible outfit combinations does stephen have for his trip?

17
8
6
144

Explanation:

Step1: Identify the multiplication principle

To find the number of outfit combinations, we use the multiplication principle of counting, which 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 there are \(m\times n\times p\) ways to do all three things together. Here, the number of ways to choose a shirt is \(8\), a pair of pants is \(6\), and a pair of shoes is \(3\).

Step2: Calculate the total combinations

Multiply the number of options for each category: \(8\times6\times3\). First, calculate \(8\times6 = 48\). Then, calculate \(48\times3=144\).

Answer:

144 (corresponding to the option with "144")