Counting Methods Review General Guidelines

Fundamental Counting Principle Each 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

General Additive Principle

Fundamental Counting Principle How 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?

Permutation How 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?

Combination How 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?

Spinner Model How 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?

Spinner Model How 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?

Complements Principle How 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?

General Additive Principle How 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