22. Scheduling AssignmentsThe starting five players for the Boston Celtics basketball team have agreed to make charity appearances tomorrow night. If you must send three players to a United Way event and the other two to a Heart Fund event, how many different ways can you make the assignments?
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26. Jumble PuzzleMany newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters AGGYB were included in newspapers on the day this exercise was written. How many ways can the letters of AGGYB be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters. AGGYB has 5 letters, so 5! = 120 ways to be arranged. BAGGY is the correct unscrambling. The probability of randomly selecting that combination of letters is 1/120.27. Coca Cola DirectorsThere are 11 members on the board of directors for the Coca Cola Company. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? Since there are four positions needed, 11 x 10 x 9 x 8 = 7.920 b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?11 = nThere are 330 possible combinations of candidates.4 = c11! Then divide by 7!4!33. PowerballAs of this writing, the Powerball lottery is run in 29 states. Winning the jackpot requires that you select the correct five numbers between 1 and 55 and, in a separate drawing, you must also select the correct single number between 1 and 42. Find the probability of winning the jackpot.55 = nThere is a 1 in 3,478,761 chance of choosing the 5 correct numbers out of 55.5 = c55!Then divide by 50!5!42 = n1 = c42!Then divide by 41!1!There is a 1 in 42 chance of selecting the correct number between 1 and42.
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