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Counting Methods Review
General Guidelines
Fundamental Counting PrincipleEach category outcome is independent of any other
category outcome OR
Items in one category can be REPEATED in another
category
Permutations
Selected items are not restricted to certain
categories but selected items MAY NOT be
repeated.Order Matters!!
Combinations
Selected items are not restricted to certain
categories but selected items MAY NOT be
repeated.Order DOES NOT matter
Spinner Models
A hybrid of the Fundamental Counting
Principle.
Complements Principle
'
Outcomes OutcomesPossible
n You n n You Don tOutcomes
Want Want
General Additive Principle
or and n n nA B A B A Bn
Fundamental Counting PrincipleHow many seven character codes can you create using only the letters A, B, C, D, E, F, G, H, I and J, where the last
character MUST be a vowel?
__ __ __ __ __ __ __
10 10 10 10 10 10 3610 3
PermutationHow many seven character codes can you create using only the letters A, B,
C, D, E, F, G, H, I and J where each letter can only be used once?
__ __ __ __ __ __ __
10 9 8 7 6 5 410 7P
CombinationHow many seven character groups can you create using only the letters A, B,
C, D, E, F, G, H, I and J where each letter can only be used once and order
doesn’t matter?
__ __ __
__ __ __ __
__ __ __10 7C
Spinner ModelHow many seven character codes can you create using only the letters A, B, C, D, E, F, G, H, I and J where the letter
D appears exactly two times?
__ __ __ __ __ __ __
2 57 21 9C
Spinner ModelHow many seven character codes can you create using only the letters A, B, C, D, E, F, G, H, I and J where a vowel
appears exactly two times?
__ __ __ __ __ __ __
2 57 23 7C
Complements PrincipleHow many seven character codes can you create using only the letters A, B, C, D, E, F, G, H, I and J where a vowel
appears at least one time?
__ __ __ __ __ __ __
7 710 7
10 10 10 10 10 10 107 7 7 7 7 7 7
General Additive PrincipleHow many ways can you choose one of the letters A, B, C, D, E, F, G, H, I
and J where the letter is either a vowel or is in the word FACE
( ) ( ) ( )
Vowel
n or nVowel n FACE nVowels in FACE
FACE
2 53 4
Vowel
n or
FACE