Lottery Combination Calculator

Calculate C(n,k) combinations for any lottery game

Calculate the number of possible combinations for any lottery game using the mathematical formula C(n,k). This tells you exactly how many different ways you can pick k numbers from a pool of n total numbers. Understanding combinations is key to grasping lottery odds.

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Enter Your Lottery Parameters

How many total numbers are in the game?
How many numbers do you need to pick?
If the game also requires choosing a separate special ball (like Powerball, Mega Ball), include the number of choices here. The final combinations will be C(n,k) × m.

Results

Total Combinations: --
Your Odds: --
Formula: C(n,k) = n! / (k! × (n-k)!)

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How Lottery Combinations Work

Lottery combinations are calculated using the mathematical formula C(n,k), which represents the number of ways to choose k items from n total items without regard to order.

C(n,k) = n! / (k! × (n-k)!)

Where:

  • n = total numbers available (the pool)
  • k = numbers you need to pick
  • ! = factorial (n! = n × (n-1) × (n-2) × ... × 1)

Examples:

  • Powerball: C(69,5) = 11,238,513 combinations (× 26 for the Powerball gives 292,201,338 unique tickets)
  • Mega Millions: C(70,5) = 12,103,014 combinations
  • Pick 3: C(10,3) = 120 combinations
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