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Select the central point, enter the numbers, and the calculator will determine their absolute deviation around the chosen central point, with step-by-step calculations.
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An online number combination calculator allows you to find the number of possible combinations from a dataset. This calculator also lists every possible combination. A combination counts the ways to select r elements from n objects where replacements are not allowed.
Read the full article to learn the combination formula, step-by-step calculations, and how to use a combinations calculator. You can also try our online permutation calculator for ordered subsets with or without repeated items.
The formula to calculate combinations is:
$$ C(n,r) = \frac{n!}{r!(n-r)!} $$
Where:
For combinations with repetition:
$$ C(n,r) = \frac{(r+n-1)!}{r!(n-1)!} $$
Use our factorial calculator for quick factorial calculations.
Select 4 students from 30 for athletics.
Solution:
$$ C(30,4) = \frac{30!}{4! \cdot 26!} = \frac{30 \cdot 29 \cdot 28 \cdot 27}{4 \cdot 3 \cdot 2 \cdot 1} = 27,405 \text{ teams} $$
Pick 6 desserts from 24 options.
Solution:
$$ C(24,6) = \frac{24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 134,596 \text{ combinations} $$
Give 3 tin cans to 8 people.
Solution:
$$ C(8,3) = \frac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1} = 56 \text{ ways} $$
When order doesn't matter (e.g., lunch: Burger, Reuben sandwich, Apple pie), it is a combination. When order matters (e.g., safe code 5-8-4), it is a permutation. A permutation is an ordered combination.
Inputs:
Outputs:
Selecting 3 elements from 10 without order or repetition, giving 120 possible combinations.
Combinations determine all possible selections where order doesn't matter, unlike permutations where order matters.
| n-CHOOSE-k | nCk |
|---|---|
| 2 choose 1 | 2 |
| 2 choose 2 | 1 |
| 3 choose 1 | 3 |
| 3 choose 2 | 3 |
| 3 choose 3 | 1 |
| 4 choose 1 | 4 |
| 4 choose 2 | 6 |
| 4 choose 3 | 4 |
| 4 choose 4 | 1 |
| 5 choose 1 | 5 |
| 5 choose 2 | 10 |
| 5 choose 3 | 10 |
| 5 choose 4 | 5 |
| 5 choose 5 | 1 |
| 6 choose 1 | 6 |
| 6 choose 2 | 15 |
| 6 choose 3 | 20 |
| 6 choose 4 | 15 |
| 6 choose 5 | 6 |
| 6 choose 6 | 1 |
Wikipedia: Combination definition & formulas
Britannica: Difference between Combination & Permutation
Math StackExchange: Find all combinations of a set
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