Prove that : n{n-1 C r-1}={n-r+1}{n C r-1}
Let A = {n-1 C r-1}
Let B = n C r-1
A = (n-1)! /{(r-1)!(n-r)!}
B = n! / {(r-1)!(n-r+1)!}
Rearranging B,
B = n(n-1)! / {(r-1)!(n-r+1)(n-r)!}
B = n(n-1)! / {(r-1)!(n-r)!(n-r+1)}
B = {n/(n-r+1)} *(n-1)! / {(r-1)!(n-r)!}
B = {n/(n-r+1)} *A
An = (n-r+1)B i.e.
n{n-1 C r-1}={n-r+1}{n C r-1}