1. Arrangements, Permutations & Combinations
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. ABC ACB AB BAC BA BCA CAB CBA
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
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB
BACD
BADC
BCAD
BCDA
BDAC
BDCA
ABC
ACB
BAC
BCA
CAB
CBA AB BA
Get at word, table of values, graph, pattern, input-output diagram
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 = 20 19 18 17 16
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