you understand how they got the denominator right?? (its just common denominator crap)
but heres some data:
r! = r (r-1)(r-2)(r-3)....= r (r-1)! hence, r!>(r-1)! by r
so basically of the r!, the (r-1)(r-2)... all cancel out which is = to (r-1)! thats why yo ucancel them, the r! is larger by...