Question

the carter family is selecting a furniture set. a furniture set has a bed, a desk and a dresser. there are 3 beds, 2 desks, and 2 dressers to select from. how many different furniture sets could they select?

Explanation:

Step1: Identify the counting principle

This is a problem of counting the number of combinations using the multiplication principle, 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.

Step2: Apply the multiplication principle

Here, the number of ways to choose a bed (\(m\)) is 3, the number of ways to choose a desk (\(n\)) is 2, and the number of ways to choose a dresser (\(p\)) is 2. So we calculate the total number of furniture sets as \(3\times2\times2\).

Step3: Calculate the result

\(3\times2\times2 = 12\).

Answer:

12