Question

lamonte is trying to pick out an outfit for the first day of school. he can choose from 8 pairs of pants, 4 t - shirts, 2 sweaters or hoodies, and 4 pairs of shoes. how many different outfits does lamonte have to choose from?

Explanation:

Step1: Identify the multiplication principle for combinations

To find the number of different outfits, we use the multiplication principle, 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 choices for pants is \( 8 \), for t - shirts is \( 4 \), for sweaters/hoodies is \( 2 \), and for shoes is \( 4 \).

Step2: Calculate the total number of outfits

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

$$\begin{align*} \text{Total outfits}&=8\times4\times2\times4\\ &=8\times4 = 32; \quad 32\times2=64; \quad 64\times4 = 256 \end{align*}$$

\]

Answer:

\( 256 \)