Question

How to solve this question?​

Answer 1

`\binom{n}{r}+\binom{n}{r+1} \\ \\ =(n!)/(r!(n-r)!) +(n!)/((n-r-1)!(r+1)!) \\ \\ =(n!(r+1))/((r+1)!(n-r)!)+(n!(n-r))/((r+1)!(n-r)!) \\ \\ =(n!(n+1))/((r+1)!(n-r)!)`

`\\ \\ =((n+1)!)/((r+1)!(n-r)!) \\ \\ =\binom{n+1}{r+1}`