In Probability, why is the denominator..(n-r)! Solution npr definition is n!/(n-r)! so the denominator is (n-r)! I\'ll explain you trhough an example. suppose there are 7 people and 5 chairs . In how many ways they can be seated? right .... first to select 5 people = 7c5 = 7! /(5! * 2!) now these 5 people can be arranged in 5! ways ( 5*4*3*2*1) so total No of ways = 7! /(5! * 2!) * 5! = 7!/2! = n!/(n-r)! this is called permutations where order of arrangement is also considered.