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Counting Unit

Counting Unit. OBJ: Review using HW 10 Review Sheet. How many different desserts are there if you have one scoop of ice cream AND one cookie? _________ • ________ Ice cream cookie 5 • 3____ Ice cream cookie 15.

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Counting Unit

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  1. Counting Unit OBJ: Review using HW 10 Review Sheet

  2. How many different desserts are there if you have one scoop of ice cream AND one cookie? _________ • ________ Ice cream cookie 5 • 3____ Ice cream cookie 15 b) How manydifferent desserts are there if you have either one scoop of ice cream OR a cookie? 8 5(ice cream) +3(cookie) 1. There are five choices of ice cream AND three choices of cookies.

  3. 2. How many different 3-letter “words” can be formed from the letters in the word CANOE? 5 • 4 • 3 = 60

  4. 3. How many different ways can 5 children arrange themselves for a game of ring-around-the- rosie? (5 – 1)! 4! 4 • 3 • 2 • 1 = 24

  5. 4. How many different ways can a teacher choose 10 homework problems from a set of 25? 25C10 25! = (25-10)! 10! 25•24•23•22•21•20•19•18•17•16•15! 15! 10•9•8•7•6•5•4•3•2•1 3,268,760

  6. 5. How many different arrangements are there of the digits 166555? 6! = 2! 3! 6 • 5 • 4 • 3! 2 • 3! 60

  7. 6. A child has 10 identically shaped blocks – 4 red, 3 green, 2 yellow, and 1 blue. How many different stacks of all 10 blocks are possible? 10! = 4! 3! 2! 1! 10 • 9 • 8•7 • 6 • 5 • 4! 4! 3 • 2 • 2 151,200 12 12,600

  8. 7. How many ways can 10 people be seated around a circular table if the host and hostess cannot be seated together? (10 – 1)! = 362,880 If the host and hostess do sit together, they would be counted as one, so now it would be asking for 9 people seated in a circle. (9 – 1)! = 8! = 40320 So to find the ways they do not sit together, subtract the two answers 9! – 8! = 362,880 – 40320 = 322,560

  9. 8. A committee of 4 is to be chosen from a club with 10 male and 12 female members. If at least 2 women must be chosen how many ways can this be done 12 C2 10C2 + 12C3 10 C1 +12C4 10 C0

  10. 13. Find the number of arrangements of the word LEVELED 7! = 3! 2! 7 • 6 • 5•4 • 3! 3! 2 840 2 420

  11. 14. How many 4 digit numbers can be made using the digits 0, 1, 2, 3, 4, 5 if repetition is not allowed? 5 • 5 • 4• 3 = 300

  12. 15. How many of them are odd? 4 • 4 • 3• 3 144

  13. 16. Do #14 if repetition is allowed 5 • 6 • 6• 6 1080

  14. 17. How many ways can you answer a 15-question always-sometimes-never geometry quiz 3 • 3 • 3• 3 • 3 • 3• 3 • 3 • 3• 3 • 3 • 3• 3 • 3 • 3 14348907

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