Algebra II
10.1: Apply the Counting Principle and
Permutations
Fundamental Counting Principle

Application of Fundamental
Counting Principle
 Ex.
1) You have 3 shirts, 4 pairs of pants,
and 2 pairs of shoes. How many outfits of
1 shirt, 1 pair of pants, and 1 pair of
shoes can you create?
Application of Fundamental
Counting Principle

Ex. 2a) How many different license plates are
possible if you have 3 letter followed by 3 digits
if digits can repeat?

2b)How many plates are possible if letters and
digits cannot repeat?
Factorial !

n! = n·(n-1)·(n-2)·(n-3)·(n-4)·…1
7!= 7·6·5·4·3·2·1
 7! = ____

Factorial
 Expand
and simplify
1.)
2.)
3.)
4.)
 An
Permutations
ordering of n objects where order is
important is a permutation of the
objects.
 The
number of permutations of n
objects is n!.
 Ex.
1a) 10 people are in a race. How
many different ways can the people finish
in the race?
Permutations

The # of permutations =
where
n = total # of objects, r = # you are taking.

Ex. 1b.) 10 people are in a race. How many
different ways can 3 people win 1st, 2nd, and
3rd place?
Ex. 2 Find the number of
permutations

Permutations with Repetition
number of permutations of n objects
where an object repeats s # of times.
 The
Find the number of distinguishable
permutations of the letters in the word.
1.) MATH
2.) TALLAHASSEE
3.) CLASSROOM
ASSIGNMENT
Find the number of distinguishable
permutations of the letters in the word.
4.) ABERDEEN
5.) CLASSROOM
6.) MATH
Permutations
 Ex.
2.) You are burning a CD with 13
songs. How many ways can the songs
be arranged on the CD?
Permutations
 Ex.
3.) Ms. Wynes’s 2nd period class is
playing 7up with a total of 19 students in
the class. How many different ways can
the people be chosen if order is
important?