Lottery Combination Calculator
Order Matters More Than It Seems
Whether you're counting lottery number groups, arranging a shortlist, or seating a committee, the same question keeps coming up: does the order of selection matter? If it doesn't — picking 6 lottery numbers is the same set regardless of the order they're drawn in — you're counting combinations. If it does — a race's 1st, 2nd, and 3rd place finishers are a different outcome depending on order — you're counting permutations. The two formulas differ by a factor that grows fast, and mixing them up leads to wildly wrong counts.
The Formula
Permutations (order matters) = n! ÷ (n−r)!
Permutations count every distinct ordering of a selection separately, while combinations group all orderings of the same selection into one count — which is why permutations of the same n and r are always equal to or larger than combinations.
Where This Matters
- Lottery number pools — standard lottery drawings use combinations, since the numbers on your ticket match regardless of the order they were physically drawn in.
- Ranked outcomes — contests with distinct 1st/2nd/3rd place prizes, or any scenario where position matters, require permutations instead.
- Verifying odds claims — if you've seen two different total counts quoted for the same n and r, checking whether each used combinations or permutations usually explains the discrepancy.
| n (pool) | r (picked) | Combinations | Permutations |
|---|---|---|---|
| 49 | 6 | 13,983,816 | 10,068,347,520 |
| 10 | 3 | 120 | 720 |
| 6 | 6 | 1 | 720 |
Notice that with n = r = 6, there's only one combination (every element is selected, so there's only one possible group), but 720 permutations — every possible ordering of those same 6 elements.
How to Use This Calculator
- Enter the total numbers in the pool (n).
- Enter the numbers picked (r).
- Select whether order matters (permutations) or order doesn't matter (combinations).
- Select Calculate for the total count.
Related Calculations
Apply this directly to a lottery drawing with the Lottery Odds Calculator, or check official Powerball odds with the Powerball Odds Calculator.