1. Permutations

2. Fundamental Principle of Counting:
If one task can be done x number of ways and another task can be done y number of ways; then the total number of ways in which these tasks can be completed together is the PRODUCT.
Example: A club consists of 15 boys and 20 girls. They wish to elect a girl as president and a boy as Vice President. They also wish to elect a Secretary and a Treasure who may be either a boy or girl.
(# choices for Pres)(# Choices for VP)(# Sec)(#Tres)
316,800 different choices

3. Permutation:
A permutation of n distinct elements taken r at a time is an ordered arrangement, without repetitions, of r of the n elements. The number of permutations of n elements taken r at a time is denoted by
Example: How many three letter combinations can be made from 26 letters if No duplication is allowed?
X X X
1st 26 choices nd 25 choices rd 24 choices

4. Factorial Notation:
Example: In how many ways can four coins be arranged in a row? (quarter, nickel, dime, penny)

5. Example:
A family of 5 consisting of the parents and 3 children are going to be arranged in a row by a photographer. If the parents are to be next to each other, how many arrangements are possible?
How many other possible ways?

6. Evaluate:

7. Using ABCDE, how many 3 letter words can be formed if repetitions are NOT allowed?
Using ABCDE, how many 3 letter words can be formed if repetitions are allowed?

8. Group Problem
If you have 5 signal flags and can send messages by hoisting one or more flags on a pole. How many messages can you send? (order matters)