Combination Calculator
Combination Calculator (nCr)
Calculate the number of possible combinations when choosing objects from a set.
n
r
C(n, r) = ?
Total Possible Combinations
0
What is a Combination?
In mathematics, a combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. You can select the items in any order, and it will still be considered the same group.
For example, if you have an apple, an orange, and a banana, and you want to choose two fruits, picking (apple, orange) is the exact same combination as picking (orange, apple).
Mathematical Formula
The standard formula to find the number of combinations is denoted by $nCr$ or $C(n, r)$, where $n$ is the total number of items, and $r$ is the number of items being chosen at a time.
Formula: $C(n, r) = \frac{n!}{r!(n-r)!}$
Frequently Asked Questions
What is the difference between a Combination and a Permutation?
The key difference lies in the order. In a Permutation, the order of the items matters (like a combination lock, where 1-2-3 is different from 3-2-1). In a Combination, the order does not matter (like a fruit salad, where an apple and a banana is the same as a banana and an apple).
Can the ‘r’ value be greater than the ‘n’ value?
No. You cannot choose more items than the total number of items available. Therefore, ‘n’ must always be greater than or equal to ‘r’.