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Pamela is planning a day out for her grandmother's birthday. They are going to have lunch at one of her grandmother's $2$ favorite restaurants, and then they will go shopping at one of her grandmother's $9$ favorite stores. Assuming the order of the activities doesn't matter, how many different ways can Pamela plan her grandmother's birthday outing? $\newline$ $\_\_\_\_\_$ ways

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Counting principle

Full solution

Q. Pamela is planning a day out for her grandmother's birthday. They are going to have lunch at one of her grandmother's

2

favorite restaurants, and then they will go shopping at one of her grandmother's

9

favorite stores. Assuming the order of the activities doesn't matter, how many different ways can Pamela plan her grandmother's birthday outing?

\newline

\_\_\_\_\_

ways

Apply Principle: Apply the Basic Counting Principle. We need to determine the total number of different ways Pamela can plan the day out. Since the choice of restaurant and the choice of store are independent events, we can multiply the number of choices for each event to find the total number of outcomes. $\newline$ Number of restaurant choices = $2$ $\newline$ Number of store choices = $9$ $\newline$ Total number of different ways = Number of restaurant choices $\times$ Number of store choices
Perform Calculation: Perform the calculation based on the Basic Counting Principle. $\newline$ $2$ (restaurants) $*$ $9$ (stores) $= 18$ $\newline$ So, there are $18$ different ways Pamela can plan her grandmother's birthday outing.

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