Question

mariana is trying to pick out an outfit for the first day of school. she can choose from 8 pairs of pants, 3 t - shirts, 4 sweaters or hoodies, and 4 pairs of shoes. how many different outfits does mariana 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 \(n_1\) ways to do one thing, \(n_2\) ways to do a second thing, \(n_3\) ways to do a third thing, and \(n_4\) ways to do a fourth thing, then the total number of ways to do all four things together is \(n_1\times n_2\times n_3\times n_4\).

Here, the number of ways to choose pants \(n_1 = 8\), t - shirts \(n_2=3\), sweaters or hoodies \(n_3 = 4\), and shoes \(n_4=4\).

Step2: Calculate the total number of outfits

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

$$\begin{align*} \text{Total number of outfits}&=8\times3\times4\times4\\ &=24\times4\times4\\ &=96\times4\\ & = 384 \end{align*}$$

\]

Answer:

384