SOLUTION: 11 books are to be stored in a shelf where 4 books can be put vertically, so they are all as easily accessible, and 6 books can be piled-up, so the most used ones are on the top.

According to the condition, 4 books on the shelf, that are stored vertically, should be considered
as unordered set. They all are "equally/easily accessible", so ordering does not matter for these 4 books.

For the set of 6 books, that are stored horizontally, there is ONLY ONE ordering "the most used ones are on the top".


Therefore, the combinatorial mechanism works as follows:


    (1)  First, we select 4 arbitrary books from 11 books and store them vertically on the left side of the shelf,
         without looking on their order.  It can be done in  = 330 different ways
         (classic combinations).


    (2)  Next, we select 6 books from remaining 11-4 = 7 books, and store them horizontally on the right side of the shelf.

         For this set of 6 books, there is only one ordering according this criterion 
         "the most used ones are on the top".  6 books from 7 can be selected in  = 7 different ways
         (classic combinations).


               +-----------------------------------------+
               |    Half of the problem is just solved.  |
               |    Now  we will solve the second half.  |
               +-----------------------------------------+


    (3)  This time, we select 6 books from 11 books and store them horizontally on the left side of the shelf.

         For this set of 6 books, there is only one ordering according this criterion 
         "the most used ones are on the top".  6 books from 11 can be selected in  = 462 different ways
         (classic combinations).


    (4)  Finally, we select 4 books from remaining 11-6 = 5 books, and store them vertically on the right side of the shelf,
         without looking on their order ("they all are easily/equally accessible").
         4 books from 5 can be selected in  = 5 different ways
         (classic combinations).


    (5)  The answer to the problems question (c) is  330*7 + 462*5 = 2310 + 2310 = 4620.



    (6)  Notice an interesting fact: the numbers of placing "vertical books on the left", 2310,
         is the same as the number of placing "vertical books on the right", precisely as it should be due to symmetry.

There are two basic options:

   1a)  We can consider the set of 4 vertical books as ordered, which means  "the order does matter and books are easily (equally ?) accessible".

   1b)  We can consider 4 vertical books are unordered set, which means "order does not matter and all books are easily (equally ?) accessible".


Which of these two interpretations to take - it is entirely on the problem's creator decision,
they both have equal rights to exist; but it should be consistent with the wording MOTIVATION around it.
Otherwise, for what reason we need this ~motivation and pronounce the words ?



The ordering of 6  horizontal books is defined by an unique way: it is ordered 
by an unique way according to the criterion "most used ones are on the top",
and there is NOTHING to discuss here.


So, the only "degree of freedom" is the choice between (1a)  and (1b).


It is what I have to say regarding your first question. 



For me, it is very important that we get agreement and common understanding with this basic issue before we will move further.


So, in your next post to me, please, let me know, if you understand everything in my writing to your question 1), 
and do you agree and do you understand everything in full in it.


Then collect 1-2 your next questions, and we will move forward.


If your questions will repeat yours #2, #3 and so on, it does not stretch me.
I only want that as we move forward, there are no unclear questions left behind our backs.