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Permutations and Combinations
EQ: What is a permutation?
Vocabulary
 Sample Space: A list of all possibly outcomes
 Tree Diagram: A visual method for counting. The last column
shows the same space
Ex
Example:
 Leah wants to make a sandwich. She has 2 types of bread, 3
cheeses, and 4 types of lunch meat. How many different
sandwiches can she make? Create a tree diagram.
Fundamental Counting Principle
 If an event M can occur m ways and is followed by N
which can occur n ways, then the even M followed by
N is equal to m‧n.
Ex) If you own 3 shirts and 5 pants, you can create 15
outfits.
Factorial (!)
 The expression n! (read n factorial) is the product of
all positive integers beginning with n and counting
backwards to 1.
5! = 5‧4‧3‧2‧1
 Ex) How many ways can 4 books be arranged on a
shelf?
Permutation
 A arrangement (or listing) in which order is important.
(example: lottery numbers, standing in line, arranging books
on a shelf)
n!
n pr 
(n  r )!
n: number of objects
r: how many you are using at a time
Examples:
1)
If there are 6 students, how many ways can you line up 4 of
them?
2)
How many ways can you arrange 4 out of 8 books on a
shelf?
Combination
 An arrangement where order is NOT important
n!
n Cr 
r!(n  r )!
n: number of objects
r: how many you are using at a time
Example:
3) How many combination of 3 letters from the set
{a,b,c,d,e}are there?
4) Sue got to pick two prizes from a grab bag of 12 prizes. How
many combinations of 2 prizes are possible?
5) How many combinations of 3 students can be made from a
class of 20?