Lesson 5.5 Combinations and Permutations Notes
Statistics
Page 1 of 3
Factorial:





In math ! is read as a factorial.
n! indicates the product of n with each of the positive counting numbers less than n.
by definition, 0! = 1
6! 6  5  4  3  2 1  720
n! nn  1n  2n  3   1
Example 1: Simplify: 7!
Example 2: Simplify: 9!
Example 3: Simplify: 8!
Example 4: Simplify:
5!
3!
Example 5: Simplify:
6!
 6  3!
Example 6: Simplify:
9!
5!  9  5 !
Permutations:



Order matters
An ordered arrangement of n distinct objects
n!
n!
Formula: n Pr 
or Pn,r 
where n is the total number of objects taken r at a
 n  r !
 n  r !
time.
Lesson 5.5 Combinations and Permutations Notes
Statistics
Page 2 of 3
Combination:


Order does not matters
n
n!
n!
Formula: n Cr 
, Cn,r 
or   where n is the total number of objects
r ! n  r !
r ! n  r  !
r
taken r at a time.
Questions to determine Combination or Permutation?
1. Does order matter?
2. How many objects do I have?
3. How many objects are being taken at a time?
Example 1: Are the following a Combination or Permutation?
a. Choosing five students from a class to work in a special project.
b. Arranging five slides in a Power Point presentation.
c. Being dealt a hand of five cards from a 52 deck of cards.
d. Arranging the letters in the word ALGEBRA.
e. Checking out 3 library books from a list of 8 books for a research paper.
f. Introducing the starting lineup at the home basketball game.
Example 2: Set up 7C2 using factorials and solve.
Example 3: Set up C12,6 using factorials and solve.
Lesson 5.5 Combinations and Permutations Notes
Statistics
Page 3 of 3
Example 4: Set up 5P3 using factorials and solve.
Example 5: Set up P9,9 using factorials and solve.
 10 
Example 6: Set up   using factorials and solve.
5
Example 7: Compute the number of possible ordered seating arrangements for eight people in five
chairs?
Example 8: In your English class, you are assigned to read any 4 books from a list of 10 books.
How many different groups of 4 are available from the list of 10?
Example 9: The board of directors at Belford Community Hospital has 12 members.
a. Three officers – president, vice president, and treasurer – must be elected from the
members. How many different slates are possible? (A slate of officers is 3 people, with the
president listed first, followed by the vice president then the treasurer.)
b. Three members from the group of 12 on the board will be selected to go to a convention (all
expenses paid) in Hawaii. How many different groups of three are possible?
Assignment: p. 192 #1, 3, 4, 6, 11, 13, 15, 17, 19, 22, 25, 27