Definition
Combination
A combination is a selection in which changing the order does not create a new result.
What it means
Ask whether rearranging the chosen items changes what was chosen. If the group stays the same, you are working with combinations. A committee of Ava and Ben is the same committee as Ben and Ava.
Remember it
Same members, same combination.
Example
Choose 2 toppings from apple, banana, and cherry, with no repeats. The combinations are {apple, banana}, {apple, cherry}, and {banana, cherry}: three choices, not six.
Watch for
A password or race result is not a combination when order changes the outcome.
Common mix-up
In a permutation, order matters; in a combination, it does not.
Exact meaning
A combination is a selection of objects for which order is irrelevant: two selections count as the same combination when they contain the same chosen objects. Whether repetition is allowed must be stated by the problem.