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Hannah makes a smoothie for breakfast every morning. Today, she wants to use $5$ different fruits. In how many different orders can she add these fruits to her blender? $\newline$ $\_\_\_\_$ orders

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Q. Hannah makes a smoothie for breakfast every morning. Today, she wants to use

5

different fruits. In how many different orders can she add these fruits to her blender?

\newline

\_\_\_\_

orders

Understand the problem: Understand the problem. $\newline$ Hannah has $5$ different fruits to add to her blender. We need to find out in how many different orders she can add these fruits. This is a permutation problem where the order matters.
Determine the formula to use: Determine the formula to use. $\newline$ Since the order in which Hannah adds the fruits matters, we will use the formula for permutations of $n$ distinct objects, which is $n!$ ( $n$ factorial).
Calculate the number of orders: Calculate the number of orders. $\newline$ Hannah has $5$ different fruits, so the number of different orders she can add them to the blender is $5!$ ( $5$ factorial). $\newline$ Number of orders = $5! = 5 \times 4 \times 3 \times 2 \times 1$
Perform the calculation: Perform the calculation. $\newline$ $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$ $\newline$ So, there are $120$ different orders in which Hannah can add the $5$ different fruits to her blender.

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