Combinations and Permutations Calculator
How many ways k items can be chosen from n, with and without counting the order.
Results
Combinations
13,983,816
Permutations
10,068,347,520
Ratio
0.000000071511
What this tool does
The defaults answer a familiar question: choosing 6 numbers from 49 gives 13 983 816 possible tickets, which is why the odds of a jackpot are what they are. The third result is that probability written as a single chance.
Formula
C(n,k) = n! ÷ (k! × (n−k)!) · P(n,k) = n! ÷ (n−k)!
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n | Total items (n) | — |
k | Items chosen (k) | — |
C | Combinations | — |
P | Permutations | — |
R | Ratio | — |
Worked example
- Total items (n)49
- Items chosen (k)6
- Combinations13,983,816
- Permutations10,068,347,520
- Ratio0.000000071511
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
Frequently asked questions
What is the difference between a combination and a permutation?
Order. A combination treats 1-2-3 and 3-2-1 as the same result; a permutation counts them separately. A lottery draw is a combination, because the order the balls come out does not change whether you won. A podium of first, second and third place is a permutation.