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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