- Consider a group of distinct individuals or objects
- “distinct” means that there is some characteristic that differentiates any particular individual or object from any other.
- How many ways are there to select a subset of size from the group?
Example
- If a Little League team has 15 players on its roster,
- how many ways are there to select 9 players to form a starting lineup?
Example
- If a university bookstore
- sells ten different laptop computers
- but has room to display only three of them,
- in how many ways can the three be chosen?
An answer to the general question just posed requires that we distinguish between two cases.
- In some situations, such as the baseball scenario, the order of selection is important.
- For example,
- Angela being the pitcher and
- Ben the catcher
- gives a different lineup from the one in which
- Angela is catcher and
- Ben is pitcher.
- For example,
- Often, though, order is not important and one is interested only in which individuals or objects are selected,
- as would be the case in the laptop display scenario.