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2. How many ways can a baseball manager arrange a batting order of 9 players? Possibilities for 1st batter = 9 Possibilities for 2nd batter = 8 Possibilities for 3rd batter = 7 9*8*7*6*5*4*3*2*1 = 9! = 362,880 5. A store manager wishes to display 8 different brands of shampoo in a row. How many ways can this be done? Possibilities for 1st bottle = 8 Possibilities for 2nd bottle = 7 Possibilities for 3rd bottle = 6 8*7*6*5*4*3*2*1 = 8! = 40,320 8. The call letters of a radio station must have 4 letters. The first letter must be a K or W. How many different station call letters can be made if repetitions are not allowed? Possibilities for 1st letter = 2 {K, W} Possibilities for 2nd letter = 25 (any letter other than your 1st letter) Possibilities for 3rd letter = 24 (any letter other than 1st or 2nd) Possibilities for 4th letter = 23 (any letter other than 1st ,2nd, or 3rd) 2*25*24*23 = 27,600 8. The call letters of a radio station must have 4 letters. The first letter must be a K or W. How many different station call letters can be made if repetitions are allowed? Possibilities for 1st letter = 2 {K, W} Possibilities for 2nd letter = 26 (any letter) Possibilities for 3rd letter = 26 (any letter) Possibilities for 4th letter = 26 (any letter) 2*26*26*26 = 35,152 10. How many different ways can 9 trophies be arranged on a shelf? Possibilities for 1st trophy = 9 Possibilities for 2nd trophy = 8 Possibilities for 3rd trophy = 7 9*8*7*6*5*4*3*2*1 = 9! = 362,880 13. Evaluate each of these: a. 8! 40,320 b. 10! 3,628,800 c. 0! 1 d. 1! 1 e. 7P5 2,520 f. 12P4 11,880 g. 5P3 60 h. 6P0 1 i. 5P5 120 j. 6P2 30 18. How many different ways can a city building inspector visit 6 buildings in the city if she visits them all in 1 day? Possibilities for 1st building = 6 Possibilities for 2nd building = 5 Possibilities for 3rd building = 4 6*5*4*3*2*1 = 6! = 720 23. How many different ways can 4 tickets be selected from 50 tickets if each ticket wins a different prize? Permutation n = 50 tickets r = 4 different prizes 50P4 = 5,527,200 24. How many different ways can a researcher select 5 rats from 20 rats and assign each to a different test? Permutation n = 20 rats r = 5 different tests 20P5 = 1,860,480 28. How many ways can 3 cards be selected from a standard deck of 52 cards disregarding the order of selection? Combination n = 52 cards r = 3 cards 52C3 = 22,100 38. Wake Up cereal comes in 2 types, crispy and crunchy. If a researcher has 10 boxes of each, how many ways can she select 3 boxes of each for a quality control test? Cripsy: Combination n = 10 boxes r = choosing 3 boxes 10C3 = 120 10C3 Crunchy: Combination n = 10 boxes r = choosing 3 boxes 10C3 * 10C3 = 120*120 = 14,400 = 120