Binomial Coefficient Calculator
The binomial coefficient calculator, commonly referred to as "n choose k", computes the number of combinations for your everyday needs.
C(10, 3)120combinations — order does not matter
Permutations P(10, 3)720order matters, so k! times larger
C(n, n−k)120always the same — choosing k is choosing which n−k to leave
Row sum 2^n1,024total subsets of n items
Pascal row 101, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1
The method
C(n, k) = n! ÷ (k!(n−k)!)
Combinations versus permutations
C(n, k) counts unordered selections; P(n, k) counts ordered ones. They differ by exactly k!, the number of ways to arrange the chosen items.
Choosing 3 from 10 gives 120 combinations but 720 permutations. Use combinations for a committee, permutations for a podium.