Analytical Geometry

• 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?

• Eg. 2 How many 4 letter sequences can be made with the vowels a,e,i,o,u & y without repeating?

• 8

• 7

• 6

• =

• 336

• 6

• 5

• 4

• =

• 3

• 360

• A Permutation is 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

• AB
• BA

• ABC
• ACB
• BAC
• BCA
• CAB
• CBA

• ABCD
• ABDC
• ACBD
• ACDB
• ADBC
• ADCB

• CABD
• CADB
• CBAD
• CBDA
• CDAC
• CDBA

• BACD
• BADC
• BCAD
• BCDA
• BDAC
• BDCA

• DABC
• DACB
• DBAC
• DBCA
• DCAB
• DCBA

• 2!= 2

• 3x2x1=3!= 6

• 4x3x2x1 = 4! = 24

• Evaluate these Factorials

• 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

• 3!

• =

• 10

• Eg. 5 Choose 5 movies from 20 on the shelf

• 20

• 19

• 18

• 17

• 16

• 5!

• 15 504

•  Because order does not matter

• Arrangements, Permutations & Combinations Challenge

• A) One chooses 3 different toppings on a tofu burger from a choice of 15 toppings.

• Arrangement, Permutation or Combination?

• Combination

• Permutation

• Arrangement

• B) Arrange all 6 shirts in your closet. Order is important.

• Combination

• Permutation

• Arrangement

• 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

• Arrangement, Permutation or Combination?

• D) Make a poker hand by taking the top 5 cards from a deck.

• Combination

• Permutation

• Arrangement

• Arrangement, Permutation or Combination?

• E) A teacher organizes all 12 class tests in order.

• Combination

• Permutation

• Arrangement

• Arrangement, Permutation or Combination?

• F) 3 cards from a deck are dealt, order is important.

• Combination

• Permutation

• Arrangement

• Arrangement, Permutation or Combination?

• G) A team of 6 horses from a batch of 12 horses are chosen.

• Combination

• Permutation

• Arrangement

• Arrangement, Permutation or Combination?

• Classwork

• pg. 232 #5-8
• Worksheet A2