Back to HW 4: 5.5

I think I understand part A (I got 445 as an answer) but I'm not quite sure how to start off part B.

For part B would it be a sum of the places you can put each book? What I mean to say is, to go along with the hint the book provides, to do 4+1-1 choose 1-1 to place first book, then 5+1-1 choose 1-1 to place second, so on, until book twelve, since as you go on, each time there is one more place you can put the next book

There are 15 total objects (books + shelves) and 3 indistinguishable objects (shelves).

Could someone quickly explain part A, i got the correct answer but it was more guess and check than actually understanding.

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Seraj Dosenbach