Mathematics

Problem

Which of the following identities holds for all integers

n \ge 1

and

1 \le r \le n

? a)

{}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n+1}C_{r+1}

{}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n+1}C_{r}

{}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n}C_{r+1}

{}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n+1}C_{r-1}