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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. - PowerPoint PPT Presentation
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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
ABBA
ABCACBBACBCACABCBA
ABCDABDCACBDACDBADBCADCB
CABDCADBCBADCBDACDACCDBA
BACDBADCBCADBCDABDACBDCA
DABCDACBDBACDBCADCABDCBA
2!= 2
3x2x1=3!= 6
4x3x2x1 = 4! = 24
Evaluate these Factorials
€
4!
€
=24
€
5!
€
8!
3!
€
11!
7!
€
9!€
=120 €
=6720
€
=7920
€
=362 880
€
10!
2!6!
€
=2520
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 #5-8Worksheet A2
