Combination Calculator (nCr)
Combination Calculator (nCr)
Enter the total number of items (n) and how many you're choosing (r). This calculates the number of combinations — the count of distinct groups of r items you can pick from n, where the order of picking doesn't matter.
Combinations show up anywhere a selection is a group rather than a sequence: choosing 6 numbers for a lottery ticket, dealing a 5-card poker hand from a 52-card deck, or picking a 3-person committee from a pool of 10 candidates. Because order is irrelevant, the combination count is always smaller than (or equal to) the corresponding permutation count for the same n and r — a useful sanity check when deciding which of the two calculators actually matches your situation.
- Formula: nCr = n! ÷ (r! × (n − r)!) — the number of unordered subsets of size r from a set of n.
- Order doesn't matter: choosing {A, B, C} is the same combination as {C, B, A} — unlike permutations, which count these separately.
- Common uses: lottery odds, poker hand counts, committee selection, and any "how many groups can I form" question.
What's the difference between combinations and permutations?
Combinations count groups regardless of order (choosing a 3-person team), while permutations count arrangements where order matters (assigning 1st/2nd/3rd place) — permutations are always larger or equal for the same n and r.
What if r is larger than n?
There are zero ways to choose more items than exist, so the result is 0 whenever r > n.
Combination Calculator (nCr)
Enter the total number of items (n) and how many you're choosing (r). This calculates the number of combinations — the count of distinct groups of r items you can pick from n, where the order of picking doesn't matter.
Combinations show up anywhere a selection is a group rather than a sequence: choosing 6 numbers for a lottery ticket, dealing a 5-card poker hand from a 52-card deck, or picking a 3-person committee from a pool of 10 candidates. Because order is irrelevant, the combination count is always smaller than (or equal to) the corresponding permutation count for the same n and r — a useful sanity check when deciding which of the two calculators actually matches your situation.
- Formula: nCr = n! ÷ (r! × (n − r)!) — the number of unordered subsets of size r from a set of n.
- Order doesn't matter: choosing {A, B, C} is the same combination as {C, B, A} — unlike permutations, which count these separately.
- Common uses: lottery odds, poker hand counts, committee selection, and any "how many groups can I form" question.
What's the difference between combinations and permutations?
Combinations count groups regardless of order (choosing a 3-person team), while permutations count arrangements where order matters (assigning 1st/2nd/3rd place) — permutations are always larger or equal for the same n and r.
What if r is larger than n?
There are zero ways to choose more items than exist, so the result is 0 whenever r > n.