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Solve by the method of your choice.
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?
There are
◻ different ways in which the prizes can be awarded.
(Simplify yous answer.)

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 yous answer.)

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Counting principle

Full solution

Q. 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 yous answer.)

Understand the problem: Understand the problem. $\newline$ We need to find the number of different ways to award three distinct prizes to three winners out of $22$ ticket holders.
Determine the method: Determine the method to use. $\newline$ Since the order in which the prizes are awarded matters (first, second, and third are distinct), we will use permutations to solve this problem.
Calculate permutations: Calculate the number of permutations. $\newline$ The number of ways to choose the first prize winner is $22$ (since there are $22$ ticket holders). After the first prize is awarded, there are $21$ ticket holders left for the second prize, and then $20$ ticket holders left for the third prize. $\newline$ The number of permutations is therefore $22 \times 21 \times 20$ .
Perform the calculation: Perform the calculation. $\newline$ Now we calculate the number of permutations: $22 \times 21 \times 20 = 9240$ .
Verify the calculation: Verify the calculation. $\newline$ To verify, we can quickly re-calculate using a calculator or by hand to ensure that $22 \times 21 \times 20$ indeed equals $9240$ .

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