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Random Integer Generator

Sampling unique random integers without replacement from a discrete pool is the mathematical foundation of lotteries, raffle ticket selection, contest

Random & Generators
integers
Change ticket # to draw again
Formula & Methodology
C(n, k) = inom{n}{k} = rac{n!}{k!(n - k)!} n = ext{Max} - ext{Min} + 1 P( ext{exact combination}) = rac{1}{C(n, k)}

The generator treats the integer interval [Min, Max] as a discrete urn containing n items. Drawing k items without replacement produces one of C(n, k) equally likely subsets. Results can be sorted numerically or viewed in draw order.

Selected Integers (6 Unique Draws)

9, 12, 19, 25, 39, 41

Overview

Sampling unique random integers without replacement from a discrete pool is the mathematical foundation of lotteries, raffle ticket selection, contest prize giveaways, and randomized cohort trials. The Random Integer Generator draws a specified subset of unique integers from any integer pool [Min, Max], sorting and presenting results instantly.

Unlike general random number tools that permit duplicate numbers, this specialized integer generator enforces strict uniqueness (sampling without replacement). It also computes the total theoretical combinations C(n, k) according to combinatorial probability theory.

Worked Examples

Example 1: Classic 6/49 Lottery Draw (Seed = 123)

Min = 1, Max = 49, Pick Count = 6, Sort = Ascending, Seed = 123

  1. Pool size n = 49 − 1 + 1 = 49 numbers.
  2. Total combinations: C(49, 6) = 13,983,816 possible tickets.
  3. Draw 6 unique integers using deterministic PRNG.
  4. Sort numbers in ascending order.
Final Answer: 7, 14, 21, 33, 40, 48 (Sum: 163 | C(49,6) = 13,983,816)

Example 2: Raffle Drawing 3 Winners from 100 Tickets (Seed = 88)

Min = 1, Max = 100, Count = 3, Sort = Ascending, Seed = 88

  1. Pool size n = 100, Pick k = 3.
  2. Combinations: C(100, 3) = (100 × 99 × 98) / 6 = 161,700.
  3. Draw 3 unique ticket numbers.
Final Answer: 23, 67, 92 (All unique winners)

Example 3: Coin Flip Simulator (1 = Heads, 2 = Tails)

Min = 1, Max = 2, Count = 1, Seed = 50

  1. Binary choice between 1 and 2.
  2. Draw single integer.
Final Answer: 2 (Tails)

How to Use This Calculator

  1. Enter the minimum and maximum boundaries of your integer pool.
  2. Specify how many unique integers to pick (Pick Count k).
  3. Choose how to sort the output (Ascending, Descending, or As Drawn).
  4. Change the Draw Ticket / Seed # to perform a new draw.

Frequently Asked Questions

Can the same integer appear more than once in the result?
No. This generator enforces strict sampling without replacement—every drawn integer in the set is guaranteed to be unique.
How are total lottery combinations calculated?
Combinations are computed using the binomial coefficient formula C(n, k) = n! / (k! * (n - k)!), which counts how many distinct groups of k items can be chosen from n items.
What is the maximum integer range supported?
You can define ranges between -1,000,000 and 1,000,000, and draw up to 100 unique integers per run.
Is this integer picker suitable for official state lotteries?
No. State lotteries require certified hardware random number generators (TRNGs) or mechanical air-mix ball machines. This is an educational and simulation tool.
How do I generate a different winning ticket?
Change the Draw Ticket / Seed # field to any other number to generate a new unique draw.

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Reviewed & Authored by: OnlineConvers Editorial Team · Last Updated: 2026-10-06
Samples discrete integers without replacement using Mulberry32 PRNG rejection sampling. Combinatorial metrics are calculated via binomial coefficient algorithms.