Binomial Coefficients Calculator

Factorial definition of binomial coefficients

For non‑negative integers \( n \) and \( k \) with \( 0 \le k \le n \):

\[ \binom{n}{k} = \frac{n!}{k! \, (n-k)!} \]

where \( m! = m \times (m-1) \times \cdots \times 2 \times 1 \) and \( 0! = 1 \).

Symmetry: \( \binom{n}{k} = \binom{n}{n-k} \).
Edge cases: \( \binom{n}{0} = \binom{n}{n} = 1 \).

Binomial coefficients: factorial method calculator

\( \displaystyle \binom{n}{k} = \frac{n!}{k!\,(n-k)!} \) → substitute n,k → evaluate

Enter exponent n (positive integer)

Binomial coefficients \( \binom{n}{k} \)

Step by step using factorial definition

References