Binomial Calculator

Calculate binomial coefficients (combinations), binomial probabilities, and related statistics.

Calculation Mode

n (total trials/items)

k (successes/selections)

1104512021025221012045101

Binomial Coefficient

C(n,k) = n! / (k!(n-k)!)

Binomial Probability

P(X=k) = C(n,k) x p^k x (1-p)^(n-k)

Binomial Coefficient C(n,k)

120

Ways to choose 3 from 10

CC(n,k)

120

PP(X=k)

11.7188%

EExpected Value

5.0000

sStd Deviation

1.5811

Expected Value E[X]

5.0000

n x p = 10 x 0.5

Variance Var(X)

2.5000

n x p x (1-p)