Section 12.9 Combinations

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 12.9

Combinations


What You Will Learn

Combinations

12.9-2


Combination

A combination is a distinct group (or set) of objects without regard to their arrangement.

12.9-3


Combination Formula

The number of combinations possible when r objects are selected from n objects is found by

nC

r

n!

n r ! r !

12.9-4


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?

12.9-5


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

12.9-6


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?

12.9-7


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

12.9-8


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?

12.9-9


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

12.9-10

Section 12.9 Combinations

Documents

Transcript of Section 12.9 Combinations