2.

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

                               =