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 your answer.)

Question

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 your answer.)

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to find the number of different ways to award three distinct prizes among 22 people. This is a permutation problem because the order in which the prizes are awarded matters.Calculate permutations: Calculate the number of permutations. The number of ways to award the first prize is 22 (since any of the 22 people can win it). After the first prize is awarded, there are 21 people left for the second prize, and after that, 20 people left for the third prize.Perform the calculation: Perform the calculation. The total number of different ways to award the prizes is the product of the number of choices for each prize: 22 choices for the first prize, 21 for the second, and 20 for the third. So, the total number of ways is 22 * 21 * 20.Calculate the product: Calculate the product. 22 * 21 * 20 = 4620Conclude the solution: Conclude the solution. There are 4620 different ways in which the prizes can be awarded.

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