Section 12.9
Combinations
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What You Will Learn
Combinations
12.9-2
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Combination
A combination is a distinct group (or
set) of objects without regard to their
arrangement.
12.9-3
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Combination Formula
The number of combinations possible
when r objects are selected from n
objects is found by
C

n r
12.9-4
n!
n  r ! r !
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Example 2: Museum Selection
While visiting New York City, the
Friedmans are interested in visiting 8
museums but have time to visit only
3. In how many ways can the
Friedmans select 3 of the 8 museums
to visit?
12.9-5
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Example 2: Museum Selection
Solution
n = 8, r = 3
8!
C


8 3
8  3 ! 3! 5! 3!


8!

8  7  6  5  4  3  2 1
5  4  3  2 1  3  2 1
 56
There are 56 different ways that 3 of
the 8 museums can be selected.
12.9-6
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Example 3: Floral Arrangements
Jan Funkhauser has 10 different cut
flowers from which she will choose 6
to use ina floral arrangement. How
many different ways can she do so?
12.9-7
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Example 3: Floral Arrangements
Solution
n = 10, r = 6
10!
C


10 6
10  6 ! 6! 4! 6!


10!
3

10  9  8  7  6  5  4  3  2 1
 210
4  3  2 1  6  5  4  3  2 1
There are 210 different ways Jan can
choose 6 cut flowers from the 10.
12.9-8
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Example 4: Dinner Combinations
At the Royal Dynasty Chinese
restaurant, dinner for eight people
consists of 3 items from column A, 4
items from column B, and 3 items
from column C. If columns A, B, and
C have 5, 7, and 6 items,
respectively, how many different
dinner combinations are possible?
12.9-9
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Example 4: Dinner Combinations
Solution
Column A: 3 of 5, Column B: 4 of 7,
Column C 3 of 6
Dinner choices  5 C3  7 C4  6 C3
 10  35  20
 7000
12.910
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