Table of Contents
Combinations Without Repetition
Combinations without repetition count the number of ways to select k items from n distinct items where each item can be chosen at most once and order doesn't matter. This is the standard "n choose k" problem and the most common type of combination.
Real-world examples include choosing lottery numbers, selecting a poker hand from a deck, picking team members from a group, and choosing toppings for a pizza from a fixed menu.
Formula
Common Examples
| Scenario | n | k | C(n,k) |
|---|---|---|---|
| Poker hand | 52 | 5 | 2,598,960 |
| Lottery 6/49 | 49 | 6 | 13,983,816 |
| Committee of 3 from 10 | 10 | 3 | 120 |
FAQ
What does "without repetition" mean?
Each item can be selected at most once. You cannot choose the same item twice. This contrasts with combinations WITH repetition where items can be reused (like scoops of ice cream from available flavors).
How does this relate to probability?
If all combinations are equally likely, the probability of any specific combination is 1/C(n,k). For example, the probability of a specific poker hand is 1/2,598,960.