## Inductive formula for binomial coefficients

In the last post on the mean and variance of a binomial random variable, we used the following formula: $$\binom{n}{k} = \binom{n-1}{k-1} + \binom{n-1}{k}.$$ Let’s just take a moment to prove this formula. Of course, how we prove it depends on what definition you use of the binomial coefficients. We have to start somewhere, after […]