Combination Without Replacement (Binomial Coefficient - n Choose k)
- is the number of UNORDERED ways of choosing π items from a set of π possible items
Formula
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where:
- π(π,π) - permutation without replacement of π items out of π total items
- π(π,π) - permutation without replacement of π items out of π total items
Formula Explanation
The only difference from Permutation Without Replacement of π items out of π total items is disregarding the order. Now the same objects sampled in a different order produce the same outcome. Thus, π(π,π) = π! different permutations (rearrangements) of the same objects yield only 1 combination. The total number of combinations is then