1 Fundamental Counting Principle & Permutations. Outcome-the result of a single trial Sample...

1 Fundamental Counting Principle & Permutations

• Outcome-the result of a single trial• Sample Space- set of all possible outcomes in

an experiment• Event- consists of 1 or more outcomes of a

trial• Independent event- each of the possibilities

does not affect the choices for the others

Fundamental Counting Principle• If event M occurs m ways, and

event N occurs n ways, then event m followed by event n occurs

m*n ways.

Example

• Many answering machines allow owners to call home and get their messages by entering a 3 digit code. How many codes are possible?

• (The choices of any of the digits doesn’t affect the other 2 digits.-Independent)

10 10 101000

1 2 3stchoice ndchoice rdchoice

Dependent event- the outcome of 1 event affects the outcome of another event

• Each player in a board game uses 1 of 6 different pieces. If 4 players play the game, how many diferent ways could players choose pieces? 6 5 4 3 360

Permutation-when a group of objects are arranged in a certain order; order matters

n distinct objects taken r at a time!

( , )( )!

nP n r

n r

Example

A newspaper has 9 reporters to cover 4 different stories. How many ways can the reporters be assigned to cover stories?

n=9 r=4 9!3024

5!

Permutation with repitionThe # of permutations of n objects of which p

are alike & q are alike is

(alike--repeaters)

!

! !

n

p q

How many different ways can the letters of the word MISSISSIPPI be arranged?

n=11(total letters) I=4S=4P=2

!

! !

n

p q

11!34650

4!4!2!

Assignment