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COMBINATION

COMBINATION

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COMBINATION

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  1. COMBINATION

  2. Combinations A combination is one of the different arrangements of a group of items where order does not matter. Where n & r are nonnegative integers & r<n

  3. Generalization • General result:This formula gives the number of subsets of size r that can be taken from a set of n objects. The order of the items in each subset does not matter. The number of combinations of n distinct objects taken r at a time without repetition is given by

  4. Other notations for C(n,r) are: Theorem 1: Theorem 2:

  5. Corollary 1: Corollary 2: Corollary 3:

  6. Corollary 4: Corollary 5:

  7. Combinations -- Special Cases There is only one way to chose 0 objects from the n objects There are n ways to select 1 object from n objects There is only one way to select n objects from n objects, and that is to choose all the objects

  8. Combinations Example Example 1:

  9. Example 2:

  10. Example. 3: How many committees of three can be selected from four people? Solution: Use A, B, C, and D to represent the people

  11. Example 4:In how many ways a committee of five can be selected from among the 80 employees of a company? Solution: Example 5:In how many ways a research worker can choose eight of the 12 largest cities in the United States to be included in a survey? Solution: