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Ethan is creating a media center. There are $2$ televisions and $6$ sets of speakers to choose from. How many different entertainment centers can Ethan make? $\newline$ $\_\_\_\_$ entertainment centers

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Counting principle

Full solution

Q. Ethan is creating a media center. There are

2

televisions and

6

sets of speakers to choose from. How many different entertainment centers can Ethan make?

\newline

\_\_\_\_

entertainment centers

Apply Basic Counting Principle: Apply the Basic Counting Principle to determine the total number of combinations. The Basic Counting Principle states that if there are $n$ ways to do one thing, and $m$ ways to do another, then there are $n \times m$ ways to do both. $\newline$ Ethan has $2$ choices for televisions and $6$ choices for sets of speakers. $\newline$ So, the total number of different entertainment centers Ethan can make is the product of the number of choices for televisions and the number of choices for speakers. $\newline$ Calculation: $2$ (televisions) $\times$ $6$ (speakers) $= 12$

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