sofia is trying to pick out an outfit for the first day of school. she can choose from 5 pairs of pants, 4 t…

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?

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?

Answer

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