Question

goran must choose a shirt, a pair of pants, and a cap for todays outfit. he has 2 shirts, 3 pairs of pants, and 2 caps to choose from. how many different outfits can he make?

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 \( m \) ways to do one thing, \( n \) ways to do a second thing, and \( p \) ways to do a third thing, then there are \( m\times n\times p \) ways to do all three things together. Here, the number of ways to choose a shirt is \( 2 \), a pair of pants is \( 3 \), and a cap is \( 2 \).

Step2: Apply the multiplication principle

We multiply the number of choices for each item: \( 2\times3\times2 \). First, calculate \( 2\times3 = 6 \), then multiply the result by \( 2 \): \( 6\times2 = 12 \).

Answer:

\( 12 \)