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Rachel is training to be a teacher and must fulfill the student teaching requirement. Rachel must be a student teacher at one of $3$ local middle schools and one of $5$ local high schools. Assuming the order doesn't matter, in how many different ways can Rachel complete the student teaching requirement? $\newline$ $\_\_\_\_$ ways

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Counting principle

Full solution

Q. Rachel is training to be a teacher and must fulfill the student teaching requirement. Rachel must be a student teacher at one of

3

local middle schools and one of

5

local high schools. Assuming the order doesn't matter, in how many different ways can Rachel complete the student teaching requirement?

\newline

\_\_\_\_

ways

Identify Options: Identify the total number of options for middle schools and high schools. $\newline$ Rachel has $3$ options for middle schools and $5$ options for high schools.
Use Counting Principle: Use the fundamental counting principle. $\newline$ The number of different ways Rachel can complete the requirement is the product of the number of options for middle schools and the number of options for high schools. $\newline$ Number of ways $= \text{Number of middle school options} \times \text{Number of high school options}$
Calculate Number of Ways: Calculate the number of different ways. $\newline$ Number of ways = $3$ (middle schools) $\times$ $5$ (high schools) = $15$ ways

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