Combination Calculator
How many ways to choose k of n items when order doesn’t matter, with the formula worked out
Combination Calculator
How to Count Combinations: n Choose k
C(n, k) = n! / (k! (n − k)!): multiply k numbers counting down from n, then divide by k!.
Example: 4 choose 2
C(4, 2) = 4! / (2! · 2!)
= (4 × 3) / (2 × 1)
= 12 / 2
= 6
| Combination | Answer |
|---|---|
| 4 choose 2 | 6 |
| 5 choose 2 | 10 |
| 3 choose 2 | 3 |
| 5 choose 3 | 10 |
| 6 choose 2 | 15 |
| 6 choose 3 | 20 |
| 4 choose 3 | 4 |
| 10 choose 2 | 45 |
| 7 choose 2 | 21 |
| 7 choose 3 | 35 |
| 8 choose 2 | 28 |
| 8 choose 4 | 70 |
Common mistakes
- k larger than n gives 0, not an error: 1 choose 3 = 0, because you can't choose 3 different items from 1. Usually the numbers were swapped — 3 choose 1 = 3.
- 0! = 1, so choosing none and choosing all are one way each: 5 choose 0 = 5 choose 5 = 1.
- If order matters, count permutations P(n, k) = n! / (n − k)! instead: 4 choose 2 = 6, but P(4, 2) = 12 — each pair counted in 2 orders.
- If items may repeat (3 scoops from 4 flavours, two of a kind allowed), use C(n + k − 1, k): C(6, 3) = 20, not 4 choose 3 = 4.
- nCr, ⁿCₖ, C(n, k) and the binomial coefficient “n over k” are the same number: 4C2 = C(4, 2) = 6.
See Also
- Random Number Generator - Pick a random whole number between two bounds
- Percent to Probability Converter - Convert Percents to "1 in X" Probability Chance
- Factors of a Number - List all Factors and Factor Pairs of a Number
Last Results
18 Choose 4: Combinations C(18, 4)
4 Choose 0: Combinations C(4, 0)
18 Choose 9: Combinations C(18, 9)
17 Choose 17: Combinations C(17, 17)
12 Choose 10: Combinations C(12, 10)
16 Choose 16: Combinations C(16, 16)
16 Choose 15: Combinations C(16, 15)
18 Choose 16: Combinations C(18, 16)
15 Choose 7: Combinations C(15, 7)
13 Choose 7: Combinations C(13, 7)
10 Choose 4: Combinations C(10, 4)
1 Choose 3: Combinations C(1, 3)
13 Choose 2: Combinations C(13, 2)
14 Choose 7: Combinations C(14, 7)
15 Choose 13: Combinations C(15, 13)
16 Choose 6: Combinations C(16, 6)
17 Choose 15: Combinations C(17, 15)
13 Choose 3: Combinations C(13, 3)
15 Choose 15: Combinations C(15, 15)
11 Choose 3: Combinations C(11, 3)
17 Choose 16: Combinations C(17, 16)
15 Choose 5: Combinations C(15, 5)
4 Choose 1: Combinations C(4, 1)
15 Choose 2: Combinations C(15, 2)
15 Choose 4: Combinations C(15, 4)
19 Choose 4: Combinations C(19, 4)
16 Choose 12: Combinations C(16, 12)
18 Choose 5: Combinations C(18, 5)
11 Choose 10: Combinations C(11, 10)
10 Choose 10: Combinations C(10, 10)
12 Choose 8: Combinations C(12, 8)
19 Choose 17: Combinations C(19, 17)
15 Choose 6: Combinations C(15, 6)
16 Choose 1: Combinations C(16, 1)
17 Choose 3: Combinations C(17, 3)
18 Choose 11: Combinations C(18, 11)
1 Choose 2: Combinations C(1, 2)
2 Choose 10: Combinations C(2, 10)
2 Choose 0: Combinations C(2, 0)
14 Choose 14: Combinations C(14, 14)
14 Choose 12: Combinations C(14, 12)
20 Choose 8: Combinations C(20, 8)
20 Choose 10: Combinations C(20, 10)
16 Choose 8: Combinations C(16, 8)
3 Choose 2: Combinations C(3, 2)
20 Choose 18: Combinations C(20, 18)
19 Choose 12: Combinations C(19, 12)
19 Choose 0: Combinations C(19, 0)
15 Choose 8: Combinations C(15, 8)
11 Choose 11: Combinations C(11, 11)
18 Choose 3: Combinations C(18, 3)
14 Choose 2: Combinations C(14, 2)
20 Choose 15: Combinations C(20, 15)
19 Choose 3: Combinations C(19, 3)
20 Choose 13: Combinations C(20, 13)
14 Choose 10: Combinations C(14, 10)