# Binomial Coefficient Calculator

Binomial coefficient is an integer that appears in the [binomial expansion] (/show/calculator/binomial-theorem). For example: \$$(a+1)^n= \binom {n} {0} a^n+ \binom {n} {1} + a^n-1+...+ \binom {n} {n} a^n \$$ We often say "n choose k" when referring to the binomial coefficient. That is because \$$\binom {n} {k} \$$ is equal to the number of distinct ways \$$k\$$ items can be picked from n items. For example, given a group of 15 footballers, there is exactly \$$\binom {15}{11} = 1365\$$ ways we can form a football team. Use this step-by-step solver to calculate the binomial coefficient.