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Luke is decorating his bedroom. There are $4$ shades of paint and $4$ styles of furniture to choose from. How many different ways can Luke customize his dorm room? $\newline$ $\_\_\_\_$ ways

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Find the number of outcomes: word problems

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Q. Luke is decorating his bedroom. There are

4

shades of paint and

4

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

\newline

\_\_\_\_

ways

Identify Options: Identify the number of options for each category. $\newline$ Luke has $4$ options for shades of paint and $4$ 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. $\newline$ $4$ (shades of paint) $\times$ $4$ (styles of furniture)
Perform Multiplication: Perform the multiplication to find the total number of combinations. $4 \times 4 = 16$

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