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Question 25, 11.3.44 points Points: 0 of 1 Save Purchase Options Question list Question 24 Question 25 Question 26 Question 27 Question 28 Solve by the method of your choice. Twenty-eight people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $5000, second prize is $4500, and third prize is $500, 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 2525, 1111.33.4444\newlinepoints\newlinePoints: 00 of 11\newlineSave\newlinePurchase Options\newlineQuestion list\newlineQuestion 2424\newlineQuestion 2525\newlineQuestion 2626\newlineQuestion 2727\newlineQuestion 2828\newlineSolve by the method of your choice.\newlineTwenty-eight people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $5000 \$ 5000 , second prize is $4500 \$ 4500 , and third prize is $500 \$ 500 , in how many different ways can the prizes be awarded?\newlineThere are □ \square different ways in which the prizes can be awarded.\newline(Simplify your answer.)

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Q. Question 2525, 1111.33.4444\newlinepoints\newlinePoints: 00 of 11\newlineSave\newlinePurchase Options\newlineQuestion list\newlineQuestion 2424\newlineQuestion 2525\newlineQuestion 2626\newlineQuestion 2727\newlineQuestion 2828\newlineSolve by the method of your choice.\newlineTwenty-eight people purchase raffle tickets. Three winning tickets are selected at random. If first prize is $5000 \$ 5000 , second prize is $4500 \$ 4500 , and third prize is $500 \$ 500 , in how many different ways can the prizes be awarded?\newlineThere are □ \square different ways in which the prizes can be awarded.\newline(Simplify your answer.)
  1. Understand the problem: Understand the problem.\newlineWe need to determine the number of different ways to award three distinct prizes to twenty-eight people. This is a permutation problem because the order in which the prizes are awarded matters.
  2. Set up the permutation formula: Set up the permutation formula.\newlineThe number of ways to award the prizes is the number of permutations of 2828 people taken 33 at a time, which is denoted as P(28,3)P(28, 3).
  3. Calculate the permutation: Calculate the permutation. \newlineP(28,3)P(28, 3) is calculated as 28!(28−3)!\frac{28!}{(28-3)!}, where ＂!＂＂!＂ denotes factorial, the product of all positive integers up to that number.
  4. Perform the calculation: Perform the calculation.\newline28!/(28−3)!=28!/25!=28×27×26×25!/25!28! / (28-3)! = 28! / 25! = 28 \times 27 \times 26 \times 25! / 25! (since the factorials cancel out)\newline=28×27×26= 28 \times 27 \times 26\newline=19656= 19656
  5. Conclude with the final answer: Conclude with the final answer.\newlineThere are 1965619656 different ways in which the prizes can be awarded.

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