[Math] How many ways 5 different books can be distributed among 10 people if each person can get any number of books

combinatorics

(Hi first time posting here so apologies if this is not the right way)

I know that the answer to this is $10^5$ but I don't really understand why this is so? Shouldn't the number of books or people be decreasing throughout the calculation? Maybe like 10P5? Or is it because of the fact that they did not distinguish between people that allows us to repeat the $10$?

Have tried looking up online and they only give the calculation.

Also is this a combination type question? Specifically something like number of combinations of $n$ distinct objects i.e. $2^n$

Thanks for taking the time to read this. Is there a better way to phrase this question so that more people can see this question without having to ask a similar question to this?

Best Answer

The first book can go to any of the $10$ persons. And then the next book can also go to any of the $10$ persons, and so on. So there are $(10)^{5}$ possibilities.

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