Permutations

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) 20 15 33 32 316,800 different choices

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 2nd 25 choices 3rd 24 choices

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

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?

Evaluate:

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?

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)