A class has 30 students. In how many ways can three prizes be awarded so that:

(a) no students get more than one prize?

(b) a student may get any number of prizes?

(a) Number of ways in which the first prize can be awarded = 30
                             m = 30
Number of eligible students for the second prize = 29
∴   Number of ways in which second prize can be awarded = 29
                         n = 29
Number of ways in which the third prize can be awarded = 28
                        P = 28
∴   By fundamental principle of counting, the total number of ways of awarding the three prizes.
              = 
(b) Number of students = 30
Number of ways in which the first prize may be awarded = 30
                    m = 30
Number of students eligible for the second prize = 30 (∵ A student may get any number of prizes)
Number of ways in which the second prize can be awarded = 30
                             n = 30
Similarly, number of ways in which the third prize can be awarded = 30
                            p = 30
By fundamental principle of counting, the number of ways in which the three prizes can be awarded
                               =