Correct!b. 2 freshmen, 3 sophomores, 1 junior, 4 seniors
I have: C(7,2)*C(7,3)*C(7,1)*C(7,4)
You're right to be uncertain. I think you've gone a bit adrift here.c. 2 each from two classes, 3 from a third class and 4 from the remaining class.
I...am not too sure about this one. I want to say C(4,2)*2*C(7,2)2*C(7,3)*C(7,4). But... like I said I am not sure.
My reasoning is that I have 4 types, I need to choose from 2 of those. Then I choose 2 from seven of each type (hence the first *2). Afterwards, I have 2 options to choose the 3 from. Hence the 2*C(7,3). Then finally I choose 4 from the last group of classmates.
It's easiest if you first choose the classes that will contribute the 3 and the 4 students, because these numbers only occur once. Then choose 2 students from each of the remaining 2 classes. So that's:OK?
OK so far, but you've then got to arrange the books within each 'object'. So you'll need to multiply by .Problem 2 is:
There are 40 books (20 Math, 15 CS, and 5 English) on a shelf, all different.
a. Fine the number of arrangements of the books in which.
1. all books in the same subject area are grouped together.
I treated each subject area as one object. So I have 3! ways to arrange those "three" objects.
Again, you have then got to arrange the CS books within their 'object'. So you'll multiply by .2. all CS books are grouped together.
I treated the CS books as one object, so I got 26!
I guess for these problems I am wanting feedback on if I am doing the problems correctly. Thanks.