Counting

A.K.A. Combinatorics

Heeley City Farm 014_edited­1 hopscotch by flickr user incurable_hippie

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

A nickel and a quarter and a dime are tossed on a table. Create a tree diagram to determine how many ways these coins can land on the table. (The order in which the coins land doesn't matter; it will next week.)

The Fundamental Principle of Counting

If 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•(n­1)•(n­2)•(n­3)• ......•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]

n! = 5 (n­2)!Given the following

Solve for n

n!(n+2)! = 12

GivenSolve for n

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

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

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

Attachments

Heeley City Farm 014_edited­1 hopscotch by flickr user incurable_hippie