Section 12.9 Combinations

What You Will Learn Combinations

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

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

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?

Example 2: Museum Selection Solution n = 8, r = 3 There are 56 different ways that 3 of the 8 museums can be selected.

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?

Example 3: Floral Arrangements Solution n = 10, r = 6 There are 210 different ways Jan can choose 6 cut flowers from the 10.

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?

Example 4: Dinner Combinations Solution Column A: 3 of 5, Column B: 4 of 7, Column C 3 of 6