combination vs permutation
Tap balls to select them and see every way they can be grouped.
One side cares about order. The other doesn't. Watch what happens.
Pick 2 or more coloured balls. The left panel shows every combination (unique groups, order ignored). The right shows every permutation (order matters). Hover or tap any arrangement to see its counterparts highlighted on the other side.
Tap balls to select them
Combinations
order doesn't matter
—
Permutations
order matters
—
Combination: "Which items?" — {A,B} is the same as {B,A}.
Permutation: "Which items, in what order?" — AB is different from BA.
A lock code is a permutation. A pizza topping choice is a combination.
Permutation: "Which items, in what order?" — AB is different from BA.
A lock code is a permutation. A pizza topping choice is a combination.
A "combination lock" is actually misnamed — it should be a "permutation lock", because 7-2-5 is different from 5-2-7.
If the order matters, it's a permutation. If you just care about which items, it's a combination.
If the order matters, it's a permutation. If you just care about which items, it's a combination.
Summary
| Combination | Permutation | |
|---|---|---|
| Order | Doesn't matter | Matters |
| Question | Which items? | Which items, in what order? |
| Count | Fewer possibilities | More possibilities |
| Formula | n! / (r! (n-r)!) | n! / (n-r)! |
| Example | Pizza toppings | Lock code |