How many ways can you choose 3 toppings from 10? Deal a 5-card hand from 52? Pick a 4-person committee from 12 volunteers? Every one of these is a binomial coefficient — "n choose k," written C(n,k) — computed as n! / (k!(n-k)!). The factorials count all orderings and then divide out the ones you do not care about, since choosing pepperoni, mushrooms, and onions is the same pizza in any order. C(10, 3) = 120 topping combos; C(52, 5) = 2,598,960 possible poker hands. The coefficients also form Pascal's triangle, where each number is the sum of the two above it, and they are the multipliers in binomial expansions. Lottery odds, card probabilities, and quality-control sampling all run on this one formula. This calculator evaluates it directly: enter your values in the Variable A and Variable B fields and read the Result. A useful symmetry to remember: C(n,k) = C(n,n-k), so choosing 3 from 10 equals choosing 7 from 10.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Binomial Coefficient Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.