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Carmen, a singer, is putting together a backup band for a recording and posted an advertisement looking for musicians. She got replies from $2$ lead guitarists and $4$ drummers. How many different backup bands is it possible for Carmen to put together? $\newline$ $\_\_\_\_$ bands

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Counting principle

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Q. Carmen, a singer, is putting together a backup band for a recording and posted an advertisement looking for musicians. She got replies from

2

lead guitarists and

4

drummers. How many different backup bands is it possible for Carmen to put together?

\newline

\_\_\_\_

bands

Apply Basic Counting Principle: Apply the Basic Counting Principle to determine the number of different backup bands Carmen can form. Since each band consists of one lead guitarist and one drummer, and the choice of a guitarist is independent of the choice of a drummer, we multiply the number of choices for each position to find the total number of different bands. $\newline$ Calculation: Number of lead guitarist choices $\times$ Number of drummer choices = $2 \times 4 = 8$

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