Transcript Algebra II

Algebra II Elements
10.4: The Fundamental Counting Principle
and Permutations
Hw: p.542 (19-22 all, 26, 56, 59, 60)
Quiz 10.4-10.6: Friday
Fundamental Counting Principle
one event occurs m ways and another
event occurs n ways, then both events
occur
ways.
 If
 (Can
be applied for more than two
events.)
Application of Fundamental
Counting Principle
 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

How many different license plates are possible
if you have 1 letter followed by 2 digits
followed by 3 letters if letters and digits can
repeat?

How many plates are possible if letters and
digits cannot repeat?
Factorial
 What
does 9! mean?
Expand and Simplify
1.)
2.)
Permutations
 An
ordering of n objects is a
permutation of the objects where
order is important.
 The
number of permutations of n
objects is n!.
Permutations

The number of permutations of r objects taken
from a group of n distinct objects is denoted by
n = total # of objects,
r = how many you are taking
We will get these answers using the calculator:
MATH button, arrow over to PRB.

Permutations
 10
people are in a race.
–How many different ways can the
people finish in the race?
–How many different ways can 3 people
win 1st, 2nd, and 3rd place?
Permutations
 You
are burning a CD with 12 songs.
How many ways can the songs be
arranged on the CD?
Permutations
 Ms.
Wynes’ 5th period class is playing
7up with a total of 18 students in the
class. How many different ways can the
people be chosen if order is important?
Permutations
 How
many different ways can you
arrange 3 out of 50 numbers to open a
locker? (Assume a number cannot be
repeated.)