Combinations answer questions like how many lottery tickets or committees are possible.
How to use the Combination Calculator
- Total items (n)
- Items chosen (r)
Results update as you type, and every field accepts the units shown in its menu.
How it works
The factorial formula is computed using log-gamma so it works for large n.
Inputs explained
| Field | What to enter |
|---|---|
| Total items (n) | A number |
| Items chosen (r) | A number |
What each result means
- Combinations = comb([Total items (n)], [Items chosen (r)])
- With repetition = comb([Total items (n)] + [Items chosen (r)] – 1, [Items chosen (r)])
- Chance of one specific combination = 1÷[Combinations]×100
Formula
C(n, r) = n! ÷ (r! (n − r)!)With repetition: C(n + r − 1, r)Worked example
Inputs — Total items (n): 49; Items chosen (r): 6.
Results — Combinations = 13983816; With repetition = 25827165; Chance of one specific combination = 0.000007 %.
Frequently asked questions
What is the difference from permutations?
Permutations count orderings; combinations ignore order.
How many 6/49 lottery combinations are there?
13,983,816.
What formula does the Combination Calculator use?
C(n, r) = n! ÷ (r! (n − r)!).