Chapter 1
Section 11-3
I CAN: Use Permutations and
Combinations
Guidelines on Which Method to Use
Permutations
Order matters!
Arrangements of n items
taken r at a time
Clue words: arrangement,
schedule, order, rank,
holding offices (Pres),
rearranging numbers
Combinations
Order doesn’t matter!
Subsets of n items taken r
at a time
Clue words: group,
sample, selection,
committee
Factorial Formula for Permutations
Arrangements are called permutations The
number of permuations of n things taken r at a
time is denoted as:
n!
n = _________________
r = _________________
n Pr

(n  r )!
.
ORDER MATTERS
n must be greater than r
*Can’t have more #s in a subset than the total # of items!
1-3-3
Example: Permutations
Evaluate each permutation.
a) 5P3
b) 10P4
Example: IDs
How many ways can you select two letters followed
by three digits for an ID if repeats are NOT
allowed? TWO PARTS!!
…or how did we do this question in 11.2?
___ ___
___ ___ ___
Example: Building Numbers From a Set
of Digits
How many four-digit numbers can be written using
the numbers from the set {1, 3, 5, 7, 9} if
repetitions are not allowed?
Factorial Formula for Combinations
In counting problems, subsets where the order
of the elements makes no difference are called
Combinations:
The # of combinations of n things taken r at a time
n Pr
n!

.
n Cr 
r ! r !(n  r )!
*ORDER DOES NOT MATTER*
Example: Combinations
Evaluate each combination.
a) 5C3
b) 7C2
Example: Finding the Number of Subsets
Find the number of different subsets of size
3 in the set {m, a, t, h, r, o, c, k, s}.
11-3-9
Example: Finding the Number of Poker
Hands
A common form of poker involves hands (sets) of five
cards each, dealt from a deck consisting of 52 different
cards. How many different 5-card hands are possible?
Repetitions are not allowed and order is not
important.
Example: Forming Committees
A city council has 8 members. The council needs to set
up a committee of 5 for a zoning issue. In how many
ways can a committee be selected?
11.3 Book Work
p. 702 #1-15 odd, 19-27 odd (skipping 17),
37, 53