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 number of different 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 \(n_1 = 5\), for t - shirts \(n_2=4\), for sweaters or hoodies \(n_3 = 7\), and for shoes \(n_4=2\).
We calculate the total number of outfits as \(5\times4\times7\times2\).
First, calculate \(5\times4=20\).
Then, calculate \(20\times7 = 140\).
Finally, calculate \(140\times2=280\).

Answer:

280