Question

sofia is trying to pick out an outfit for the first day of school. she can choose from 5 pairs of pants, 4 t - shirts, 7 sweaters or hoodies, and 2 pairs of shoes. how many different outfits does sofia have to choose from?

Explanation:

Step1: Identify the multiplication principle

To find the total number of outfits, we use the multiplication principle of counting, which states that if there are \(n_1\) ways to do the first task, \(n_2\) ways to do the second task, \(n_3\) ways to do the third task, and \(n_4\) ways to do the fourth task, then the total number of ways to do all four tasks together is \(n_1\times n_2\times n_3\times n_4\). Here, the tasks are choosing pants, t - shirts, sweaters/hoodies, and shoes.

Step2: Multiply the number of choices for each item

The number of choices for pants (\(n_1\)) is 5, for t - shirts (\(n_2\)) is 4, for sweaters/hoodies (\(n_3\)) is 7, and for shoes (\(n_4\)) is 2.
So the total number of outfits \(N=5\times4\times7\times2\).
First, calculate \(5\times4 = 20\). Then, \(20\times7=140\). Finally, \(140\times2 = 280\).

Answer:

280