1. 10.4 counting and perumtations.notebook March 27, 2013
How many lunch specials can you choose from if you can choose chicken,
pasta or fish as a main dish and soup or salad as a side dish?
Fundamental Counting Principle:
Two Events Three Events
m n m n p

2. 10.4 counting and perumtations.notebook March 27, 2013
You are ordering a case for your MP3 player. You can choose any of 30 colors
for the main shell, and of 32 colors for the protective band, and any of 200
decals for the cover screen. How many different cases are possible?

3. 10.4 counting and perumtations.notebook March 27, 2013
You are choosing a password that has 4 letters followed by 2 digits.
How many passwords are possible if the letters and digits can be repeated?
How many passwords are possible if the letters and digits cannot be repeated?

4. 10.4 counting and perumtations.notebook March 27, 2013
Permutations ­ an ordering of a set of objects
There are 6 permutations of the Letters A, B, and C
ABC ACB BAC BCA CAB CBA
By the counting principle: ___ ___ ___
The number of permutations of n distinct objects is n!.
Examples
4! 5! 6!

5. 10.4 counting and perumtations.notebook March 27, 2013
Eight skiers are competing in a moguls (snow bumps) competition.
In how many different orders can the skiers finish the competition?
In how many different ways can 3 of the skiers finish first through third?

6. 10.4 counting and perumtations.notebook March 27, 2013
In the second question above, an ordered group of 3 skiers is taken from the group of 8 skiers.
This is a permutation of 8 objects taken 3 at a time. It is denoted by 8P3. Or . . .
P =
8 3
n!
The number of permutations of n objects taken r at a time is denoted by nPr =
(n ­ r)!

7. 10.4 counting and perumtations.notebook March 27, 2013
You have 6 text messages on your cell phone. In how many
orders can you reply to 4 of the messages? to all 6?