Combination Calculator (nCr)
Calculate the number of possible selections when order does not matter.
Combinations (nCr): —
Combination formula: nCr = n! / [ r! (n − r)! ]
Example
If you have 5 balls and choose 3 without caring about order:
n = 5
r = 3
Combinations = 10
What does this calculator do?
It calculates how many unique groups of r items can be selected from n distinct items when order does not matter.
When should you use combinations?
Use combinations when selecting items where order is irrelevant, such as lottery numbers, committees, or groups.
Frequently Asked Questions
What is the difference between combinations and permutations?
Permutations consider order, while combinations do not.
Can r be greater than n?
No. The number of selected items cannot exceed the total number of items.
Is the result always an integer?
Yes. Combination counts are always whole numbers.