# Discrete math counting principles. In how many ways can a teacher distribute 12 identical science books among 15 students if 1) no student gets more than one book? 2) if the oldest student gets two books but no other student gets more than one book?

Discrete math counting principles
In how many ways can a teacher distribute 12 identical science books among 15 students if
1) no student gets more than one book?
2) if the oldest student gets two books but no other student gets more than one book?
Initially, I tried the binomial theorems with the idea that the student gets a book or no book but that is not giving me the correct solution.
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Kaiden Weeks
Step 1
Hint for 1) Count the number of subsets of cardinality 12 of a set of 15 elements.
Step 2
Hint for 2) Count the number of subsets of cardinality $12-2$ of a set of $15-1$ elements.
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agantisbz
Step 1
Assuming the students are distinguishable:
For the first one: If no student gets more than one book, then it is just a matter of finding the number of ways to pick 12 students out of those 15, i.e. $\left(\genfrac{}{}{0}{}{15}{12}\right)$
Step 2
For the second one: the oldest one gets 2 books ... leaving 14 students ... and 10 books ... can you do the rest?
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