Combinations calculate the number of ways to choose k items from n items where order does not matter.
⚠n and k must be non-negative integers, k ≤ n. Large values will show in scientific notation.
What is Combination?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select items in any order.
Order Doesn't Matter
AB = BA - same selection, different order counts as one
Formula
C(n,k) = n! / (k!(n-k)!) where n ≥ k ≥ 0
Binomial Coefficient
C(n,k) is the coefficient in binomial expansion (a+b)ⁿ
Symmetry
C(n,k) = C(n,n-k), choosing k is same as choosing n-k to exclude
💡 Example: C(10,4) = 10! / (4! × 6!) = 3628800 / (24 × 720) = 210. There are 210 ways to choose 4 items from 10.
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