How to differentiate the usage of "number" in situations that "number" represents "index" and "quantity" respectively

Question

Number has both meaning of "index" and "quantity". I am often confused by this in writing sentences such as:

The conversion between the number of books and total pages is simple. (quantity)
The number of book on that shelf is 5 counting from left. (index)

My questions are:

Is the second sentence grammatically correct?
How to discriminate these two scenarios?

UPDATE:
According to this dictionary, number can be used as "position in series" or "quantity". For sentence:
Room number is 5

Is that correct to turn this statement into questions like:
what is the number of room? (what position)

As Stuart comments: "Using singular vs plural indicates whether you're talking about book number 5 or five books.", if I want to question the quantity of rooms, should I say:
what is the number of rooms? (what quantity)

Steve · Answer

Grammatically, for the singular 'index' sense, you would typically ask "what is the room number?, or "what is the number of the room?".
For the plural index sense, you would ask "what are the room numbers?", or "what are the numbers of the rooms?".
When asking a similar question in the quantitative sense, you often don't use the word "number", but simply ask "how many rooms?".
You could ask "what is the number of rooms?", but this is generally considered an improper phrasing.
If you are expressing a statement rather than asking a question, for the index sense you would say "the room number is five".
For the quantitative sense you would say "the rooms number five", but here the word "number" is used as a verb, and this phrasing tends to be considered literary, rhetorical, or emphatic.
It's not uncommon in administrative contexts to find abbreviated questions.  For the index sense: "room number?", "room numbers?", "number of room?", and (unconventionally) "numbers of rooms?".
For the quantitative sense: "number of rooms?".
These cases are distinguished fundamentally when number is singular whilst rooms is plural - in other words, you're asking about one number in relation to many rooms, which can only mean the quantity.

How to differentiate the usage of "number" in situations that "number" represents "index" and "quantity" respectively

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