Algebra and Trigonometry, 5th Edition

11.6 Combinatorics: Combinations

• Evaluate combination notation and solve related applied problems.

We now consider counting techniques in which order is not considered.

Combinations

We sometimes make a selection from a set without regard to order. Such a selection is called a combination. If you play cards, for example, you know that in most situations the order in which you hold cards is not important. That is,

Each hand contains the same combination of three cards.

Example 1

Find all the combinations of 3 letters taken from the set of 5 letters $\{\text{A},\text{B},\text{C},\text{D},\text{E}\}$.

Solution

The combinations are

$$\begin{array}{rc}\{\text{A},\text{ B},\text{ C}\},& \{\text{A},\text{ B},\text{ D}\},\\ \{\text{A},\text{ B},\text{ E}\},& \{\text{A}\end{array}$$