Question

There are 30 students in a class, 3 prizes are to be awarded to the students. In how many
different ways can be prizes be awarded if (i) no student is to be awarded more than one
prize ? (ii) a student can receive any number of prizes?
can you please provide me step by step explanation​

Answer 1

Step-by-step explanation:

(i): To award 1st price we have 30 choices.

To award 2nd price we have (30-1=29) choices, as we have already given 1st place to one of the students.

To award 3rd price we have (29-1) choices, we have loose two choice when we choose 1st & 2nd place.

Total number of ways = 30 x 29 x 28

= 24360

(ii): In the first case, we award students with unique prize. But here we have 30 choices for all the awards.

Total number of ways = 30 x 30 x 30

= 27000