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Lesson #36 Arrangements, Permutations & Combinations

Lesson #36 Arrangements, Permutations & Combinations. An Arrangement is an ordered sequence of items where not every item is used. Eg 1 . How many ways can 8 athletes receive gold, silver and bronze medals?. 8. 7. 6. =. 336.

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Lesson #36 Arrangements, Permutations & Combinations

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  1. Lesson #36 Arrangements, Permutations & Combinations

  2. An Arrangement is an ordered sequence of items where not every item is used. • Eg 1. How many ways can 8 athletes receive gold, silver and bronze medals? • 8 • 7 • 6 • = • 336 • Eg. 2 How many 4 letter sequences can be made with the vowels a,e,i,o,u & y without repeating? • 6 • 5 • 4 • 3 • 360 • =

  3. A Permutationis an ordered arrangement where ALL • of the items in a set are used. • Eg.3 List the permutations of students at the front • 2 students • 3 students • 4 students • ABCD • ABDC • ACBD • ACDB • ADBC • ADCB • BACD • BADC • BCAD • BCDA • BDAC • BDCA • ABC • ACB • BAC • BCA • CAB • CBA • AB • BA • CABD • CADB • CBAD • CBDA • CDAC • CDBA • DABC • DACB • DBAC • DBCA • DCAB • DCBA • 2!= 2 • 3x2x1=3!= 6 • 4x3x2x1 = 4! = 24

  4. Evaluate these Factorials

  5. A Combination is an arrangement of some of the • items are chosen. The order does NOT matter. • It should really be called • a permutation lock! • Eg. 4 Choose 3 students from a set of 5 to go to the office • 5 • 4 • 3 • = • 10 • 3! •  Because order does not matter • Eg. 5 Choose 5 movies from 20 on the shelf • = • 16 • 20 • 19 • 18 • 17 • 15 504 • 5!

  6. Arrangements, Permutations & Combinations Challenge

  7. Arrangement, Permutation or Combination? A) One chooses 3 different toppings on a tofu burger from a choice of 15 toppings. Combination Permutation Arrangement

  8. Arrangement, Permutation or Combination? B) Arrange all 6 shirts in your closet. Order is important. Combination Permutation Arrangement

  9. Arrangement, Permutation or Combination? C) Take your two favourite movies from a collection of 15 dvds to a friend’s for a slumber party. Combination Permutation Arrangement

  10. Arrangement, Permutation or Combination? D) Make a poker hand by taking the top 5 cards from a deck. Combination Permutation Arrangement

  11. Arrangement, Permutation or Combination? E) A teacher organizes all 12 class tests in order. Combination Permutation Arrangement

  12. Arrangement, Permutation or Combination? F) 3 cards from a deck are dealt, order is important. Combination Permutation Arrangement

  13. Arrangement, Permutation or Combination? G) A team of 6 horses from a batch of 12 horses are chosen. Combination Permutation Arrangement

  14. Classwork pg. 232 #5-8 Worksheet A2

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