I read What is Mathematics book by Richard Courant and Herbert Robbins and there is an exercise where I should prove the Binomial theorem using induction. Here is an expression to be proved: $$ C^n_i = \frac{n(n-1)(n-2)...(n - i + 1)}{1 * 2 * 3 ... i} = \frac{n!}{i!(n - i)!} $$
I will be grateful for any help you can provide