Question

in how many ways can 5 prizes be distributed to 8 students if each student can get any number of prizes?

Answer 1

Each student can get any number of prizes:

⇒ Each prize can be given to any of the 8 students

⇒ one prize = 8C1 = 8 ways

Each student can receive any number of prizes:

⇒ 8C1 x 8C1  x 8C1 x  8C1 x 8C1  ways

⇒ 8 x 8 x 8 x 8 x 8

⇒ 8⁵

⇒ 32768

Answer: There are 32768 ways of distributing the 8 prizes to 5 students.

Answer 2

here is your answer OK dude

A prize can be given to any one of the 8 students in (8/1)=8 ways

So, each prize can be distributed in (8/1)=8 ways

5 prizes can be distributed in (8/1)×(8/1)×(8/1)×(8/1)×(8/1)
= 8 power 5

I hope it helps!