Picking Winners Fairly: Combinations for Raffles and Giveaways

Combinations vs. Permutations

When prizes are identical, the draw produces a set of winners, so use combinations: C(200,3) = 200 × 199 × 198 ÷ 6 = 1,313,400. For ranked prizes, order matters, so use permutations: P(200,3) = 7,880,400.

The ratio is 3! = 6, the number of ways to arrange the same three winners.

Running a Fair Draw

Assign each entry a number from 1 to 200 and use a random number generator to pick values within that range. If a number repeats, discard it and draw again so that nobody wins twice. For a transparent draw, record the process, or draw live on video.

Do not use a method with built-in bias, such as picking the nth person on a list or the entry closest to a time. Avoid the modulo trap, where taking a large random number modulo 200 slightly favors small numbers if the generator's range is not a multiple of 200. Quality tools sidestep this problem.

• Number every entry once.
• Use a trustworthy random source.
• Reject duplicates when drawing without replacement.
• Document the date, tool, and seed or result.

Odds With Multiple Entries

If one person buys several entries, their chance rises in proportion. With 10 of the 200 entries, the chance of winning at least one of 3 prizes is 1 − C(190,3) ÷ C(200,3) = 1 − 1,125,180 ÷ 1,313,400 ≈ 14.3%.

Check local laws before running a raffle or giveaway, since rules on prize drawings differ by region and often require registration or a free entry route.