Question 1204816
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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 : 
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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 ?



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<U>Comment from student</U>: &nbsp;&nbsp;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!



<U>My response</U>.  &nbsp;&nbsp;It looks like this problem is &nbsp;SELF-CONTRADICTORY, or, &nbsp;at least, &nbsp;poorly worded.


Report to your professor, &nbsp;or to the author of the textbook, &nbsp;or to the publishing company 

or to other source as a web-site about this deficiency.



They will award you for your vigilance.



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



At this forum, &nbsp;significant part of &nbsp;" problems " &nbsp;is written &nbsp;(is created and composed) 

by persons whose mathematical education is from reading puzzles.