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.

Question 1204816: 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.
(a) In how many ways the books can be put in vertical positions?
Your answer is :
(b) In how many ways the books can be piled-up?
Your answer is :
(c) In how many ways the books can be put in both positions?
Your answer is :
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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.
(a) In how many ways the books can be put in vertical positions?
Your answer is :
(b) In how many ways the books can be piled-up?
Your answer is :
(c) In how many ways the books can be put in both positions?
Your answer is :
~~~~~~~~~~~~~~~~~~~~~~~~~

Hello, 4 + 6 = 10; but the post tells us about 11 books.

Where is the 11-th book ?   Is it missed ?   stolen ?   annihilated ?   remains outside the shelf ?

--------------------

Comment from student:   that's exactly why i cannot solve this, i was thinking there is
something wrong with me but seems like an issue with my prof i guess. thanks!

My response.   It looks like this problem is SELF-CONTRADICTORY, or, at least, poorly worded.

Report to your professor, or to the author of the textbook, or to the publishing company
or to other source as a web-site about this deficiency.

They will award you for your vigilance.

\\\\\\\\\\\\\\\\\\\\\

By the way, it easily can be that the problem assumes that one book may remain outside.

But, if so, it should be clear from the problem's formulation.
It should not be as a reader's guess.
In other words, in this case problem's wording should be different.

Always remember that Math problem and puzzle are different things.

What is allowed in puzzles is not always allowed in Math problems.

In puzzles, the major goal is to perplex a reader, making the problem's description
confusing and ambiguous.

In Math problems, the major goal is to TEACH a reader, making the problem description
as straight, as clear, as precise and as unambiguous as possible, so that any questions
“ what is this ” and “ why is this so ” would not arise at all.

At this forum, significant part of " problems " is written (is created and composed)
by persons whose mathematical education is from reading puzzles.

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