Final answer:
Using the concept of combinations with repetitions, there are precisely 792 ways in which 5 prizes can be distributed amongst 8 students where each student can receive any number of prizes, including zero.
Step-by-step explanation:
The subject of this question is within the domain of Combinatorics, specifically looking at problems of distribution or partition, in the field of Mathematics. An important concept to understand here is the bars and stars method or combination with repetition.
In this case, we have a total of 5 prizes (stars) and 8 students (spaces between bars or bins), and each student can receive any number of prizes, including zero. This can be framed as a question of how many ways there are to place the prizes (stars) into 8 categories (spaces between bars), which includes having some categories with no stars if a student receives no prizes.
To solve this, the formula to use is the combination with repetition formula, (n + r - 1)C(r), where n represents the number of categories (in this case, the students) and r represents the items being categorized (in this case, the prizes). Therefore, substituting n = 8 and r = 5 into the formula would give us (8 + 5 - 1)C(5) = 792 ways.
So, the answer is neither (a) 5 ways (b) 8 ways (c) 256 ways nor (d) Infinite ways. The correct number of ways would be 792.
Learn more about Combinations with Repetition