Question
There are three prizes to be distributed among 6 students. In how many ways can this be done when
(a) no boy gets more than one prize.
(b) there is no restriction as to the number of prizes that a boy may get.
(c) no boy sets all prizes.
Solution
(a) n = 6, r = 3
Number of permutations = 
Hence, the number of ways, in which the three prizes can be awarded = 120.
(b) n = 6, r = 3
Number of permutations = 
Hence, the number of ways in which 3 prizes can be awarded = 216.
(c) Number of ways in which one boy gets all prizes = number of boys = n = 6.
