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•1
0! = 1
Examples:
4! = 4•3•2•1
4! = 24 On the calculator:
[MATH] [<] [4]
Examples:
6! = 6•5•4•3•2•1
6! = 720

Given the following
Solve for n
n! = 5 (n­2)!

Given
(n+2)! Solve for n
= 12
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