1. 11.8 Combinations A combination of items occurs when
The items are selected from the same group.
No item is used more than once.
The order of items makes no difference.
Note:
Permutation problems involve situations in which order matters.
Combination problems involve situations in which the order of items makes no difference.

2. Examples 1 – 2: Determine which involve permutations and which involve combinations.
Example 1: Six students are running for student government president, vice-president and treasure. The student with the greatest number of votes becomes the president, the second highest vote-getter becomes vice-president, and the student who gets the third largest number of votes will be treasurer. How many different outcomes are possible?
Example 2: Six people are on the board of supervisors for your neighborhood park. A three-person committee is needed to study the possibility of expanding the park. How many different committees could be formed from the six people?

3. Comparing Combinations and Permutations
Given the letters: A,B,C,D: We can compare how many
permutations and how many combinations are possible if
we chose 3 letters at a time:

4. The number of possible combinations if r items are taken from n items is:
Example 3: 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?

5. Example 4: Jan Funkhauser has 10 different cut flowers from which she will choose 6 to use in a floral arrangement. How many different ways can she do so?
Example 5: How many three-person committees could be formed from 8 people?

6. Example 6: 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?
Example 7: In December, 2009, the U.S Senate consisted of 60 Democrats and 40 Republicans. How many committees can be formed if each committee must have 3 Democrats and 2 Republicans?