Table of Contents
What Are Combinations?
A combination is a selection of items from a larger set where the order does not matter. For example, choosing 3 fruits from a basket of 10 different fruits. The key distinction from permutations is that {apple, banana, cherry} is the same combination as {cherry, apple, banana}.
Combinations are used extensively in probability theory, lottery calculations, committee formation, and any scenario where you need to count the number of ways to select a subset from a larger set without regard to arrangement.
Formulas
With repetition allowed:
Combinations vs Permutations
| Feature | Combination | Permutation |
|---|---|---|
| Order matters? | No | Yes |
| Example | Lottery numbers | PIN codes |
| C(5,3) vs P(5,3) | 10 | 60 |
| Formula | n!/(r!(n-r)!) | n!/(n-r)! |
Frequently Asked Questions
When should I use combinations vs permutations?
Use combinations when the order of selection does not matter (e.g., choosing team members, lottery draws). Use permutations when order matters (e.g., arranging books on a shelf, creating passwords, ranking contestants).
What does "with repetition" mean?
With repetition means items can be selected more than once. For example, when creating a 4-digit PIN, each digit (0-9) can be repeated. Without repetition, once an item is selected, it cannot be chosen again.