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Stanley wants to plant $5$ different types of flowers in his garden this year. If he plants one type of flower each morning, in how many different orders could the flowers be planted? $\newline$ _____ orders

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Q. Stanley wants to plant

5

different types of flowers in his garden this year. If he plants one type of flower each morning, in how many different orders could the flowers be planted?

\newline

_____ orders

Understand the problem: Understand the problem. $\newline$ Stanley has $5$ different types of flowers to plant. He wants to know in how many different orders he can plant them if he plants one type each morning.
Recognize the problem type: Recognize that the problem is a permutation problem. Since the order in which the flowers are planted matters, we are dealing with permutations. The number of different orders in which $5$ items can be arranged is given by the factorial of the number of items, which is $5!$ ( $5$ factorial).
Calculate $5!$ : Calculate the value of $5!$ . $\newline$ The factorial of a number $n$ , denoted by $n!$ , is the product of all positive integers less than or equal to $n$ . $\newline$ $5! = 5 \times 4 \times 3 \times 2 \times 1$
Perform the multiplication: Perform the multiplication to find the number of orders. $\newline$ $5! = 5 \times 4 \times 3 \times 2 \times 1$ $\newline$ $= 120$

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