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Permutations
&
Combinations
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Independent Events
events that do not affect each other
Dependent Events
events that affect each other
(the outcome of one event DEPENDS on the other event)
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Example 1
Determine whether the events are independent or dependent
1. choosing an ice cream flavor and choosing a topping for
the ice cream
2. from 15 entries in an art contest, a teacher chooses
first, second, and third place
3. 75 tickets are placed in a jar. 3 tickets are selected,
one after the other, without replacing a ticket after it is
chosen
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Fundamental Counting Principle
Suppose one event can be chosen in p ways,
and another independent event can be chosen
in q different ways,. Then the two events can be
chosen successively in pq ways.
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Example 2
1. Mary brought 8 t's and 6 shorts to camp. How many different outfits consisting of
a t-shirt and a pair of shorts does she have?
2. How many 5-digit even numbers can be formed using the digits 4,6,7,2,8 if digits
can be repeated?
3. How many license plates consisting of 3 letters followed by 3 numbers are
possible if repetition is allowed?
4. In how many different ways can 4 different books be arranged on the shelf?
5. The top 5 runners at the cross country meet will receive trophies. If there are 22
runners, in how many ways can the trophies be awarded?
6. How many license plates consisting of 3 letters followed by 3 numbers are
possible if repetition is not allowed?
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PERMUTATION
the arrangement of objects in a particular order
n objects chosen r at a time
nPr
or P(n,r)
Entering on the Calculator:
n, MATH, move to PRB column, choice #2, r
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Example 3
1. P(6,6)
2. P(11,6)
3. P(6,4)
P(5,3)
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Example 4
1. A math teacher needs to place five books--algebra I, algebra II, geometry,
algebra III, and calculus--on her bookshelf. How many ways can the books be
displayed on the shelf?
How many ways can she display just 3 of the books?
2. A high school honor society is composed of 7 students. How many different
ways can all the members stand in line for a picture?
How many ways can they select a president and vice-president?
3. The high school chorus has been practicing 12 songs, but there is time for
only 5 at the spring concert. How many different orderings of 5 songs are
possible?
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COMBINATION
the arrangement of objects where the order is not a
consideration
n objects chosen r at a time
nC r
or C(n,r)
Entering on the Calculator:
n, MATH, move to PRB column, choice #3, r
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Example 5
1. C(7,7)
2. C(8,6)
3. C(3,2) C(5,3)
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Example 6
1. How many groups of 4 students can be selected from a
class of 20?
2. Every year, a popular magazine picks 15 top-rated tv
movies of the previous year. A network wants to select 3 out of
these 15 movies to show during the month of August. How
many groups of 3 movies can be selected?
3. From a standard deck of 52 cards, how many 5 card poker
hands can be drawn?
4. From a group of 10 men and 12 women, how many
committees of 5 men and 6 women be formed?
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5. At Lincoln High, there are 10 names on the ballot for
senior class officers. Four will be selected to form a
committee.
a) How many different committees of 4 can be formed?
b) In how many ways can a committee of 4 be formed if
each student has a different responsibility?
c) If there are 6 girls and 4 boys on the ballot, how many
committees of 3 girls and 1 boy be formed?
HOMEWORK
p. 843 (16-38 evens, 40-48)
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