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