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