I would like to meet on Tuesdays from 3-5 and work on this homework as a group. As of right now, meeting in the Union is the best meeting point. I'll be seated next to Starbucks and will bring my book. Please call or text me at 317-605-6720 with any questions or comments. Hopefully we can work through some of these problems together. Ryan Hossler

HW4MA375S10

5.5 - 10, 18, 20, 24, 44, 46, 50, 54, 62

Section 5.5

10.

18. How do we account for the overcount?

Think of what happens in a string when you switch a 1 and another 1. The string does not change.

20.

I am looking to check my answer on this one. I got 78, did anyone else get something different?

yes, I got something different. remember that it is less than or equal to 11 not just equal to 11. look at the hint. it should help a lot.

24.

44.

Anyone have any ideas for 44b? This could be way off, but is the answer 4*12!^12 because there are 12! ways to place the books in specific order on each shelf, 12 places on the shelves for books (there can be any number on each shelf, but only 12 books can be used), and 4 shelves for the books to rest on?

Look at question 45, then the answer to it in the back of the book.

I don't even understand answer on the book.

46.

Does anyone have an idea or a hint to help me on this one? It seems like we talked about this in class but for some reason i can not find it in my notes.

50.

54.

Anyone know how to do this one?

look at example 11 in section 5.5

62. does anyone have hints on this? I think I might have gotten part-way through this. The total number of terms equals the number of solutions to x1+x2+...+xm = n, because in each term, the exponents have to add up to n. Then you could do the stars and bars method, where you have m-1 bars and n stars. That leads you to C(n+m-1, m-1). However, this is where I am stuck; I have no idea how to account for the terms that can be combined. I was thinking maybe none can be combined? But probably not because the question mentioned them.

I can't help much because I too am stuck but I have gotten to the same point you have so I believe it just takes a little tinkering with the data to get the final answer.

I tested this out for (x+y+z)^2 and used m=3 and n=2. When you multiply it out by hand you get 6 different terms and C(3+2-1,2-1)= C(4,2)= 6. So I don't think you need to worry about the combined terms. I think it accounts for it. The equation you have above x1+x2+x3+...+xm=n can also be thought of as the number of different combinations the exponents can be that all add up to n. Like with the binomial thereom, the term is always there just it may not show because the exponent could be 0 resulting in the term to equal 1. Thinking about it this way makes sense that there would be no need to think of overcount with the combined terms.