Twenty two people purchase raffle tickets. Three winning tickets are selected at random if the first prize is $1000, the second prize is $500, and the 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 (Simplily your answer).

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Identify the problem: Identify the problem. We need to determine the number of different ways to award three distinct prizes among twenty-two people.Determine the approach: Determine the approach. Since the prizes are distinct, we can use permutations to calculate the number of ways to award the prizes. The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of items, and r is the number of items to choose.Calculate first prize: Calculate the number of ways to award the first prize. There are 22 people and only one first prize, so there are 22 ways to award the first prize.Calculate second prize: Calculate the number of ways to award the second prize. After awarding the first prize, there are 21 people left. So, there are 21 ways to award the second prize.Calculate third prize: Calculate the number of ways to award the third prize. After awarding the first and second prizes, there are 20 people left. So, there are 20 ways to award the third prize.Calculate total ways: Calculate the total number of different ways to award the three prizes. To find the total number of ways to award the three prizes, we multiply the number of ways to award each prize together: 22 * 21 * 20.Perform calculation: Perform the calculation. 22 * 21 * 20 = 9,240.Conclude solution: Conclude the solution. There are 9,240 different ways in which the prizes can be awarded.

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