## 12.2 Outline

- Committee problem
- definition
- combination formula
- deck of cards

- Pascal’s triangle
*n*choose*r*- table entries

- Counting with the binomial theorem
- binomial theorem
- number of subsets

## 12.2 Essential Ideas

**Combinations **A combination of

*r*elements selected from a set of

*n*elements is an subset of

*r*elements selected

*without repetitions*. The order of selection is not important.

**Counting Formulas**

**Combination formula:** The number of ways of selecting *r* elements from a set with cardinality *n* in which the order of selection is not important is *n!/r!(n − r)!*.

**Combinations by Pascal’s Triangle **The number of ways of selecting

*r*elements from a set with cardinality

*n*in which the order of selection is not important is found by looking at the

*r*th entry in the

*n*row: