Binomial coefficient

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The binomial coefficients are defined by the formula $${n \choose k} = \dfrac{n!}{(n-k)!k!}.$$

Properties

Theorem (Binomial Theorem): $(a+b)^n = \displaystyle\sum_{k=0}^n {n \choose k} a^k b^{n-k}$

Proof:

References

Abramowitz and Stegun