copyright 2013, 2010, 2007, pearson, education, inc. section 12.9 combinations
TRANSCRIPT
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 12.9
Combinations
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
Combinations
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Combination
A combination is a distinct group (or set) of objects without regard to their arrangement.
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Combination Formula
The number of combinations possible when r objects are selected from n objects is found by
nC
r
n!
n r ! r !
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Example 2: Museum SelectionWhile 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?
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 2: Museum SelectionSolutionn = 8, r = 3
There are 56 different ways that 3 of the 8 museums can be selected.
8C
3
8!
8 3 ! 3!
8!
5! 3!
8 7 6 5 4 32 1
5 4 32 1 32 1 56
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Example 3: Floral ArrangementsJan 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?
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Example 3: Floral ArrangementsSolutionn = 10, r = 6
There are 210 different ways Jan can choose 6 cut flowers from the 10.
10
C6
10!
10 6 ! 6!
10!
4! 6!
10 93
8 7 6 5 4 32 1
4 3 2 16 5 4 32 1 210
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Example 4: Dinner CombinationsAt 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?
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Example 4: Dinner CombinationsSolutionColumn A: 3 of 5, Column B: 4 of 7, Column C 3 of 6
Dinner choices 5C
3
7C
4
6C
3
10 35 20
7000
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