# Pre Calculus 12

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Im on the chapter of permutations/combinations/fundamental counting principle

need help with 2 questions

1. emma is arranging her books in piles on her desk. she has 5 math books, 3 english books, and 4 science books. how many ways can she arrange them if she wants to keep the subject areas 2gether?

I did 12!/4!3!5!, but that's wrong, it should be 360 :|

2. gordon has some spare change on his desk, he got a nickel, penny and quarter. assumin that he uses at least 1 coin, how many diff sums r possible?

^ i did 3P1 * 3P1 * 3P1, but the answer is supposed to be 12 :|

• Pre Calculus 12 - ,

There are 3! ways to arrange the subjects
For each such arrangement, there are 5! * 3! * 4! ways to arrange the books.

That would be 3!3!4!5! = 103680
No idea how 360 is the answer.
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C(3,1)+C(3,2)+C(3,3) = 3+3+1
No idea how 12 is the answer. The coins can be picked in the following ways:

p,n,q, pn,pq,nq, pnq
The order does not matter.