If this is what you mean, then:
(500 nPr 400)/(500 nPr 100)*(1/400 nPr 300) =1
simplify | ((500!)/((500 - 400)!))/((500!)/((500 - 100)!))×1/((400!)/((400 - 300)!))
=(500!/(500-400)! x (500-100)!/500!=(100!*400!) * 1/(400!)*(100!)
=(100!*400!) / (100!*400!) =1
