Introduction to combinatorics and the fundamental principal of counting.

1. Counting
A.K.A.
Combinatorics
Heeley City Farm 014_edited-1 hopscotch by flickr user incurable_hippie

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

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

5. 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?

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

7. Factorial Notation
Definition:
n! = n•(n-1)•(n-2)•(n-3)• ......•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

8. Simplify

10. Simplify

11. 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

12. 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

13. (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?