Question

Determine the number of ways in which 5 prizes can be distributed among 4 students.

• A. 4⁵
• B. 5⁴
• C. 20
• D. 5!/4

Answer 1

The correct option is A 4⁵

Suppose there were no restrictions whatsoever and the problem simply said "How can you distribute k prizes among p students?".

For each prize, there are p possibilities for the recipient of that prize. In total, that means there are p⋅p⋅.....⋅p (with k copies of p in the product) possible ways to assign the prizes. This is the $p^k$ part.

Or, we can say. This is a type of “Different to Different” question.

5 prizes can be distributed among 4 students in $4^5$ ways.