Question

Prove that (n-1, r)+(n, r-1)=(n,r)​

Answer 1

Answer:

$\binom{n - 1}{r} + \binom{n}{r - 1} = \binom{n}{r} \\( n - 1) + n = n \\ n - 1 = 0 \\ n = 1 \\ r + (r - 1) = r \\ r = 1 \\ \binom{0}{1} + \binom{1}{0} = \binom{1}{1}$