estion list $\newline$ Question $23$ $\newline$ Question $24$ $\newline$ Question $25$ $\newline$ uestion $26$ $\newline$ Solve by the method of your choice. $\newline$ Twenty-two people purchase raffle tickets. Three winning tickets are selected at random. If first prize is \$$1000$, second prize is \$$500$, and third prize is \$$100$, in how many different ways can the prizes be awarded?$\newline$There are $\square$ different ways in which the prizes can be awarded.$\newline$(Simplify your answer.)

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Grade 8

Multiply and divide rational numbers: word problems

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Q. estion list

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Question

23

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24

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Question

25

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uestion

26

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Solve by the method of your choice.

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Twenty-two people purchase raffle tickets. Three winning tickets are selected at random. If first prize is \$$1000$, second prize is \$$500$, and third prize is \$$100$, in how many different ways can the prizes be awarded?$\newline$There are $\square$ different ways in which the prizes can be awarded.$\newline$(Simplify your answer.)

Identify Problem Type: Identify the problem as a permutation since the order in which the prizes are awarded matters. There are $22$ people and $3$ prizes, so we need to calculate the number of ways to choose $3$ winners out of $22$ where the order is important.
Use Permutations Formula: Use the formula for permutations, which is $P(n, k) = \frac{n!}{(n - k)!}$ , where $n$ is the total number of items and $k$ is the number of items to choose. Here, $n$ is $22$ and $k$ is $3$ .
Calculate Permutation: Calculate the permutation: $P(22, 3) = \frac{22!}{(22 - 3)!} = \frac{22!}{19!}$ .
Simplify Expression: Simplify the expression by canceling out the common factorial terms: $\frac{22!}{19!} = 22 \times 21 \times 20$ .
Perform Multiplication: Perform the multiplication: $22 \times 21 \times 20 = 9240$ .