#first course in probability #sheldon_ross 8th edition Qn. #12(a)

Question

Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30. How many different outcomes are possible if (a) a student can receive any number of awards?

Answer 1

1st prize can be distributed to any of 30 students=30 ways

2nd  .....................................................................=30 ways

3rd.......................................................................=30 ways

4th.......................................................................=30 ways

5th.......................................................................=30 ways

total = 30*30*30*30*30=24300000 ways

Answer 2

It is saying selected students from a class of 30.

Let s be the number of selected students. Now, s can be selected from 30 in 30Cs ways. It is also given that each student can receive any number of awards, maximum awards a student can receive is 5. So s student can receive s⁵ awards.

So, number of different outcomes possible are = 30Cs * s⁵