Counting

A.K.A. Combinatorics

Heeley City Farm 014_edited-1 hopscotch by flickr user incurable_hippie

Three coins are tossed on a table. Create a tree diagram to determine how many ways these coins can land on the table.

In how many ways can 5 people be seated in a straight line?

The Fundamental Principle of CountingIf there are M ways to do a first thing and N ways to do a second thing, then there are M x N ways to do both things.

Example: How many outfits can be made from 3 pants and 4 shirts?

In how many ways can six students be seated in 8 vacant seats?

Factorial Notation

Definition:n! = n•(n-1)•(n-2)•(n-3)• ......•3•2•10! = 1

Examples:4! = 4•3•2•14! = 24

Examples:6! = 6•5•4•3•2•16! = 720

On the calculator:[MATH] [<] [4]

Simplify

Simplify

How many phone numbers can be made under the following conditions:

(First digit cannot be 0 or 1 because you'll get the operator or long distance.) • The first two digits are 3 followed by 6 • The third digit is even • The fourth digit is greater than 5 • The fifth and seventh digits are odd • The sixth digit is 2

How many phone numbers can be made under the following conditions:

(First digit cannot be 0 or 1 because you'll get the operator or long distance.) • The first two digits are 3 followed by 6 • The third digit is even • The fourth digit is greater than 5 • The fifth and seventh digits are odd • The sixth digit is 2

(a) How many “words” of 4 different letters each can be made from the letters A, E, I, O, R, S, T?

(c) In how many of these words do vowels and consonants alternate?

(b) How many of these words begin with a vowel and end with a consonant?