MTH 232
Section 14.3
Permutations and Combinations
Overview
• Another consideration of counting is whether
or not order matters in selecting items from a
set:
• An organization with 10 members wants to
select a president and vice-president.
• An organization with 10 members wants to
select two members to attend a conference.
Permutation: Arrangement
• The permutation of r objects chosen from a
set of n elements is given by:
n!
P(n, r ) 
(n  r )!
Combination: Selection
• The combination of r objects chosen from a
set of n elements is given by:
n!
C (n, r ) 
r!(n  r )!
What’s The Deal With The Exclamation
Point?
• No, it doesn’t mean that the number is
excited…
• ! Means “factorial”:
0! = 1 (by definition)
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
Let’s Practice
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•
•
•
C(7, 3)
C(7, 7)
P(8, 5)
P(8, 8)
How Do You Tell Which One To Use?
• Ask yourself, “Does order matter?”
• If yes, use Permutation
• If no, use Combination
Examples
• Phi Theta Kappa has 20 members. How many ways can
a president, vice-president, and secretary be chosen?
• The Ambassadors have 20 members, 12 male and 8
female.
1. How many ways can they line up for a group picture?
2. How many ways can they line up for a group picture if
males are on the back row and females are on the
front row?
3. How many ways can three Ambassadors be selected
to serve as organization representatives in a collegewide assembly?