Binomial coefficient: Decrement identities

Dependencies:

1. Binomial Coefficient

\[ \binom{n}{k} = \frac{n}{k} \binom{n-1}{k-1} = \frac{n}{n-k} \binom{n-1}{k} = \frac{n-k+1}{k} \binom{n}{k-1} \]

Proof

Simple algebraic manipulation using the fact that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$.

Dependency for:

1. Binomial coefficient: Bulk decrement

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Binomial Coefficient