What's the relationship between combination and polynomial equation? I mean, I am not able to grasp certain points here or let's say connect them into a whole:
1. Take a question where it's asked that we have to arrange 10 books : 4 of A, 3 of B, 2 of C, and 1 of D in such a way that each book of similar type remain with its own type so like AAAABBBDCCC, etc. Here we are doing 4!*4!*3!*2!*1!.
2. When we take a question of dividing 10 police officers into 3 groups: 10 -> 5,3,2. Here we use 10!/*5!*3!*2!).
3. How many solutions of $x1+x2+x3+...+xn=300$ are possible?
Doubt: What's the difference between 1 & 2? Isn't two equivalent to saying arrange 10 officers like manner of AAAAABBBCC? If we are grouping 10 distinct elements into 3 groups where each group is of same type, then what's the catch here?
Second is what's the similarity between 2 and 3? Isn't three equivalent to saying group 300 distinct element into 3 bags/groups?
I am totally confuse here and I think I cannot move ahead with my GATE preparation if I cannot clear my doubt on combinatorics which in turn would mean no way of doing probability's tricky questions.
EDIT: Here's the images of different questions. How do I differentiate between them?