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Luke is going in for a checkup at a large medical clinic. Luke will meet with one of the $2$ physician assistants and be examined by one of the $4$ doctors. How many different ways might Luke have a checkup? $\newline$ $\_\_\_\_\_$ ways

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Find the number of outcomes: word problems

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Q. Luke is going in for a checkup at a large medical clinic. Luke will meet with one of the

2

physician assistants and be examined by one of the

4

doctors. How many different ways might Luke have a checkup?

\newline

\_\_\_\_\_

ways

Introduction: To determine the number of different ways Luke might have a checkup, we need to consider the number of physician assistants and the number of doctors available. Since Luke will meet with one physician assistant and one doctor, we can use the fundamental counting principle, which 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.
Physician Assistant: First, let's consider the number of ways Luke can meet with a physician assistant. There are $2$ physician assistants available, so there are $2$ different ways he can meet with a physician assistant.
Doctor: Next, let's consider the number of ways Luke can be examined by a doctor. There are $4$ doctors available, so there are $4$ different ways he can be examined by a doctor.
Total Number of Ways: Now, we multiply the number of ways to meet with a physician assistant by the number of ways to be examined by a doctor to find the total number of different ways Luke can have a checkup. $\newline$ $2$ (ways to meet with a physician assistant) $*$ $4$ (ways to be examined by a doctor) $=$ $8$ different ways.

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