Combinations Calculator (nCr)

Combinations Calculator

Calculate nCr - Order doesn't matter - Selections where sequence is irrelevant

Permutations
Combinations
Active Formula

Result

5C3

10

Interpretation

Possible selections of 3 items from 5

Understanding Permutations vs Combinations

The key difference is whether order matters. Use permutations when the sequence or arrangement is important, and combinations when you only care about which items are selected.

Permutations (nPr)
  • Order matters: ABC ≠ BAC
  • Examples: Race rankings, password sequences
  • Formula:
Combinations (nCr)
  • Order doesn't matter: ABC = BAC
  • Examples: Team selection, lottery numbers
  • Formula:

Combinations Guide

How to Use

  1. 1Enter the total number of items (n).
  2. 2Enter the number of items to choose (r).
  3. 3Click Calculate to find value of C(n, r).
  4. 4Remember: In combinations, ORDER DOES NOT MATTER.

Formula & Logic

A combination is a selection of items from a collection, such that the order of selection does not matter.

n= Total items in the set
r= Items chosen
!= Factorial

Practical Applications

1

Lottery

Calculate the odds of winning a lottery where you choose numbers and order doesn't matter.

2

Team Selection

Determine how many ways a committee can be formed from a larger group of people.

3

Card Games

Calculate the number of possible poker hands dealt from a standard deck.

Frequently Asked Questions

QWhat is the difference between Permutation and Combination?

For Combinations, order implies nothing (ABC = CBA). For Permutations, order changes the identity of the set (ABC ≠ CBA).

QDoes repetition matter?

Standard nCr calculations assume no repetition is allowed (you cannot pick the same item twice). There are separate formulas for combinations with repetition.

QCan r be larger than n?

No, you cannot choose more items than are available in the total set. r must be less than or equal to n.