This is not a homework question, just more of a question that sort of had me scratching my head. Although I'm in upper level math courses I honestly don't remember much about permutation or combinations, but I believe this question is solved using one or both of these. Searching for similar questions online didn't turn up much help.
There are x+y different books on the shelf, x books have blue binding, and y books have white bindings.
a) how many ways can the books be arranged so that the books with blue bindings occupy the first x positions?
b) how many ways can we arrange the books so the books with blue bindings are together?
My attempt at it for (a) was $\frac{(x+y)!}{((x+y)-x)!}$ But after doing that I wasn't sure. I didn't even attempt (b).
a)Take two strings, one whith only $x$ blue letters and one with only $y$ white letters, if you glue those two together you get a string with $x+y$ letters with the first $x$ blue. So you have $x!y!$ different strings.
b) If I understood the question you have to put all the blue books on the shelf together.
You have $y+1$ (thank's to grand_chat) spaces to put the books and then you have the same problem as above, so $(y+1)(x!y!)$