Question

diane must choose a shirt and a pair of pants for todays outfit. she has 2 shirts and 4 pairs of pants to choose from. how many different outfits can she make?

Explanation:

Step1: Identify the counting principle

This is a problem of the fundamental counting principle, where if there are \( m \) ways to do one thing and \( n \) ways to do another, the total number of ways to do both is \( m\times n \). Here, the number of ways to choose a shirt is \( 2 \), and the number of ways to choose a pair of pants is \( 4 \).

Step2: Calculate the total number of outfits

Using the fundamental counting principle, we multiply the number of shirt choices by the number of pants choices. So, the total number of different outfits is \( 2\times4 \).
\[
2\times4 = 8
\]

Answer:

\( 8 \)