Permutations and Combinations
Combinations and permutations count how many ways you can choose or arrange items. The difference is whether the order matters. Pick the type and enter n and r.
Your numbers
Result
- Formula
- C(5,2) = 5! / [2! · (5-2)!]
| Step | Detail |
|---|---|
| Type | Combination (order does not matter) |
| Formula | C(5,2) = 5! / [2! · (5-2)!] |
| Result | 10 |
Combination vs permutation
In a combination the order does not matter — {A, B} is the same as {B, A}: C(n,r) = n! / [r! (n-r)!]. In a permutation the order does matter — AB differs from BA: P(n,r) = n! / (n-r)!. So permutations are always greater than or equal to combinations. For n=5, r=2: nPr = 20, nCr = 10.
How to choose
Ask: does order change the outcome? A podium or a password depends on order → permutation. Picking a committee or a lottery set does not → combination. Spotting that is the key step in any counting problem.
Frequently asked questions
Sources
- Combinatorics — permutations and combinations
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