The document discusses counting principles and permutations. It explains that if there are M ways to do the first thing and N ways to do the second, then there are MxN ways to do both. It then provides examples of counting outfits from different numbers of pants and shirts, and counting the possible arrangements of coins landing on a table.

1. Today's special in the cafeteria offers you a choice of 2 main dishes and one of
3 different drinks. How many different meals can you order?

2. The Fundamental Principle of Counting
If there are M 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?

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

5. 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.

6. Factorial Notation ...
Definition:
n! = n•(n-1)•(n-2)•(n-3) ...... 3•2•1.
0! = 1
Examples:
On the calculator:
4! = 4•3•2•1
[MATH] [<] [4]
4! = 24
6! = 6•5•4•3•2•1
6! = 720

7. Simplify each of the following ...

8. How many different three digit numbers can be made using the seven digits 1,
2, 3, 4, 5, 6, 7, without repetition?
Using the same 7 digits as above how many digits can be made if the three digit
number must be even.
How many of the three digit numbers are odd?
How many of the three digit numbers are greater than 300?

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