11.7 Fundamental Counting Principles

Example

- A) password has 2 lowercase letter and 4 digits -no repetition of letters and numbers - 26 x 25 x 10 x 9 x 8 x 7 = 3,276,000 - B) first letter must be a vowel (5) - first digit cannot be 0 5 x 25 x 9 x 9 x 8 x 7 = 567,000

Example

- taking a 5 question multiple choice test , each problem has 4 choices, answer every question, how many ways? - 4 x 4 x 4 x 4 x 4 = 1024 ways

Example

-3 skirts , 5 blouses, 2 pairs of shoes. How many diff outfits are possible? - 3 x 5 x 2 = 30 diff outfits

Fundamental Counting Principle

-m experiment x n experiment - more than one category - multiply - n1 x n2 x n3 x n4 ......

Example

-password has 2 lowercase letters and 4 digits, repetition is permitted. How many diff passwords? - 26 x 26 x 10 x10 x10 x10 = 6,760,000 diff ways

with or without

2 choices