- #1

- 996

- 5

If a total of 5 distinct awards are distributed among 30 students where any student can receive more than 1 award, how many possible outcomes are there?

2. Homework Equations

[tex] \text{outcomes} = r^n [/tex]

where r is the number of choices and n is the number of draws.

3. The Attempt at a Solution

I know the answer is [itex]30^5[/itex] but I don't see why 30 is the number of choices and 5 is the number of draws. I know in the case of how many numbers can be formed using 8 binary digits is [itex]2^8[/itex]. In this case it kind of makes sense that there are only two choices (0 or 1) and I perform the operation 8 times, but with the award and student problem is confusing to me. I just don't see how 30 is the number of choices. I can just as easily say 5 is the number of choices; a student can have up to 5 awards. Only the other hand, only 1 student could get 5 awards, so it really isn't the same as the binary number problem.

What is the thought process to properly sort this out? I've also seen explanations in terms of bins and balls but it's tough to figure out which is the bin and which is the ball. There is something conceptually I'm not getting. Can someone explain?