Question

alexa is trying to pick out an outfit for the first day of school. she can choose from 8 pairs of pants, 6 t - shirts, 6 sweaters or hoodies, and 2 pairs of shoes. how many different outfits does alexa have to choose from?

Explanation:

Step1: Identify the multiplication principle

To find the number of different outfits, 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, \(p\) ways to do a third thing, and \(q\) ways to do a fourth thing, then the total number of ways to do all four things together is \(m\times n\times p\times q\). Here, the number of ways to choose pants is \(8\), t - shirts is \(6\), sweaters/hoodies is \(6\), and shoes is \(2\).

Step2: Calculate the total number of outfits

We multiply the number of choices for each category:
\[

$$\begin{align*} \text{Total outfits}&=8\times6\times6\times2\\ & = 8\times6\times12\\ &=8\times72\\ & = 576 \end{align*}$$

\]

Answer:

\(576\)