Try an Example
Pick a scenario to see how the calculator works, then adjust the values
Lottery Draw
Calculate the number of possible 6/49 lottery combinations.
Key values: Total balls: 49 · Drawn: 6 · Combination mode
Race Podium
Find the number of ways to award Gold, Silver, and Bronze among 8 runners.
Key values: Runners: 8 · Medals: 3 · Permutation mode
Secret Santa
Calculate valid gift assignments where nobody draws their own name.
Key values: Participants: 8 · Derangement mode
Password Keyspace
Estimate the number of possible 8-character passwords from printable ASCII.
Key values: Character set: 94 · Length: 8 · Repetition allowed
This calculator is also known as Lottery Combination Calculator.
Read the complete guideWhy Lottery Uses Combinations
Lottery draws use combinations because the order in which balls are drawn does not matter. Drawing 3-7-15 is the same ticket as 15-3-7. This is why the formula C(n,r) applies.
Examples
6/49 Lottery
Standard 6/49 lottery draw
C(49,6) = 13,983,816 -- your chance of a jackpot is about 1 in 14 million.
Key takeaway: You are more likely to be struck by lightning twice than to win a 6/49 lottery.
Understanding Lottery Odds
Key facts about lottery probabilities:
- Each additional ball drawn multiplies the denominator of your odds
- Adding a bonus ball pool (like Powerball) multiplies the total combinations further
- The expected value of a lottery ticket is almost always negative
Frequently Asked Questions about Lottery Combination Calculator
Why are lottery odds so extreme?
Lottery odds are calculated using combinations because the order of drawn balls does not matter. C(49,6) = 13,983,816 means there are nearly 14 million possible tickets, but only one wins the jackpot.
Does the order in which lottery balls are drawn matter?
No. Drawing 1-2-3-4-5-6 is the same ticket as 6-5-4-3-2-1, so combinations apply. If order did matter, there would be P(49,6) = 10,068,347,520 outcomes -- over 700 times more -- and the odds would be even worse.
How do Powerball odds compare to a standard 6/49 lottery?
Powerball draws 5 numbers from 69 white balls [C(69,5) = 11,238,513] plus 1 Powerball from 26 red balls. Total combinations = 11,238,513 × 26 = 292,201,338, giving jackpot odds of about 1 in 292 million -- roughly 20 times harder than 6/49.
Specialized Calculators
Choose from 6 specialized versions of this calculator, each optimized for specific use cases and calculation methods.
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