Prove that nc_r/nc_r-1=n-r+1/r

(ⁿC_r-1) = n! / (r-1)! ( n- (r-1))!

⇒ n! / (r-1)! (n-r+1)!

⇒ n! / (r-1)! (n-r)! (n-r+1).......................(1) and 

⇒ ⁿC_r= n! / r! (n-r)! 

⇒ n! / r (r-1)! (n-r)!.....................(2)

dividing (2) by (1) we get

ⁿC_r-1/ ⁿC_r= n-r+1/ r since other terms cancel out

Hence proved.