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Damon is decorating his bedroom. There are $3$ shades of paint and $5$ styles of furniture to choose from. How many different ways can Damon customize his dorm room? $\newline$ $\_\_\_\_$ ways

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Counting principle

Full solution

Q. Damon is decorating his bedroom. There are

3

shades of paint and

5

styles of furniture to choose from. How many different ways can Damon customize his dorm room?

\newline

\_\_\_\_

ways

Identify Options: Identify the number of options for each category. $\newline$ Damon has $3$ options for shades of paint and $5$ options for styles of furniture.
Use Counting Principle: Use the fundamental counting principle. $\newline$ To find the total number of different combinations, we multiply the number of options for paint by the number of options for furniture. $\newline$ Total combinations = Number of paint options $\times$ Number of furniture options
Perform Calculation: Perform the calculation. $\newline$ Total combinations = $3$ (shades of paint) $\times$ $5$ (styles of furniture) $\newline$ Total combinations = $15$

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