1 Fundamental Counting Principle & Permutations. Outcome-the result of a single trial Sample Space- set of all possible outcomes in an experiment Event-

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Presentation transcript:

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)

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?

Permutation-when a group of objects are arranged in a certain order; order matters n distinct objects taken r at a time

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

Permutation with repition The # of permutations of n objects of which p are alike & q are alike is (alike--repeaters)

How many different ways can the letters of the word MISSISSIPPI be arranged? n=11(total letters) I=4 S=4 P=2

Assignment