Combinations Calculator

Combinations Calculator
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About Combinations

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

For example, given four letters: A, B, C and D there are six combinations of two that can be drawn from this collection:

  • A and B
  • A and C
  • A and D
  • B and C
  • B and D
  • C and D

Thus, the number of possible combinations of 2 samples from a 4 item collection is 6.

Unlike permutations, combinations consider the order of the sample not relevant.

Combinations Formula

The formula for combinations is:
C(n,k) = n! / [ k! (n-k)! ] Where n is the collection size and k is the sample size.

Combinations Example

A lotto game has 50 balls numbered from 1 to 50. 5 balls are drawn (without reposition) to get the winning key. How many possible keys exist ?

C(50,5) = 50! / [ 5! (50-5)! ] = 2,118,760

For more info on Combinations: https://en.wikipedia.org/wiki/Combination


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