Practice Each event can occur in the given number of ways. Find the number of ways all of the events can occur. Event 1: 3 ways, Event 2: 7 ways 21 ways Event 1: 8 ways, Event 2: 5 ways 40 ways Event 1: 4 ways, Event 2: 2 ways, Event 3: 9 ways 72 ways Event 1: 6 ways, Event 2: 7 ways, Event 3: 4 ways 168 ways For the given configuration, determine how many different computer passwords are possible if (a) digits and letters can be repeated, and (b) digits and letters cannot be repeated. 3 digits followed by 4 letters a) 456,976,000 b) 258,336,000 2 digits followed by 5 letters a) 1,188,137,600 b) 710,424,000 1 letter followed by 6 digits a) 26,000,000 b) 3,931,200 4 letters followed by 4 digits a) 4,569,760,000 b) 1,808,352,000 Evaluate the expression. 5! 120 10! 3,628,800 9! 362,880 14!/11! 8,720 30! / 29! 30 4! * 6! 17,280 7! / 5! 420 11! / (6! * 2!) 990 17. P(4, 2) = 12 18. P(5, 2) = 20 19. P(4, 4) = 24 20. P(5, 5) = 120 21. P(7, 3) = 210 22. P(6, 4) = 360 23. P(7, 5) = 2,520 24. P(12, 4) = 479,001,600 **Find the number of distinguishable permutations of the letters in the word.** 25. MATH: 24 26. SOUTH: 120 27. BALL: 12 28. ODD: 3 29. SPANISH: 2,520 30. MINNESOTA: 181,440 31. DELAWARE: 10,080 32. LETTERS: 1,260 33. Men's Suits: A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants. How many different suits consisting of a jacket, shirt, tie, and pants are possible? 576 suits 34. Batting Order: A baseball manager is determining the batting order for the team. The team has 9 players, but the manager definitely wants the pitcher to bat last. How many batting orders are possible? 40,320 batting orders 35. Chores: Your chores for the week are to cut the grass, wash the car, clean your room, clean the garage, and shine your shoes. You are to do 1 chore each day from Monday through Friday. You can do each chore on whatever day you want, except that you must wash the car either Thursday or Friday. In how many different orders can you perform your chores? 48 ways

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