In my current project I want to translate the phrase "a large number of tents are set up." This is part of the text of a video game, specifically the narration. But looking at dict.cc, I see numerous ways to say "number of [something]":
I do not know which to use as I am not sure how these differ, if at all.
There's a very easy and natural way of using Anzahl that you didn't mention:
You just use Anzahl and then, directly following, the noun in nominative or genitive case. It can be used just like a measurement unit, e.g. "ein Kilo Erbsen" or "drei Paletten Radios".
Eine große Anzahl Zelte wird aufgebaut.
Die Jugendlichen schliefen in einer großen Anzahl Zelte, die direkt hinter dem Strand aufgestellt worden waren.
Comments on the options that were mentioned in the question:
It's not wrong, but I would avoid this and use:
This is the preposition to use if you want to use a preposition for some reason.
You use this if you want to refer to a definite set of [noun] with a definite article, like in:
Die Anzahl der Fahrraddiebstähle, bei denen kein Täter ermittelt werden kann, steigt seit Jahren.
equivalent to Anzahl, there's no real difference. The use without article or prepositions (eine Zahl Zelte) is uncommon with "Zahl" though.
Yes, you can create that or use it if you know that it is already in use, but you would normally only create that if you really want it to be a term that's going to be used at least a few times. For example, if you write a study comparing scout summer camps, you might want to refer to their "Zeltzahl" in your statistics.
This is derived from the meaning "a row of ..." and it doesn't talk about a number at all, it's basically synonymous to "some". You can also just use this with a noun in nominative: "eine Reihe Zelte".
None of your given translations has a counterpart for large.
The simplest variant would of course be viele [noun], e. g. viele Zelte.
Note, that eine Reihe von corresponds to a few or a couple of, so the number is below large.
I think the most natural translation for
A large number of tents are set up.
is
Zahlreiche Zelte werden aufgebaut.
It sounds eloquent to say:
Eine Vielzahl von Zelten wurde aufgestellt. In my mind, this evokes the image of a site with many different tents, like a campground. If the tents all look the same, like at a base camp, I would rather say: Eine große Anzahl von Zelten wurde aufgestellt.
A large number of tents are set up there.
For quantifyable numbers, use Zahl, not Anzahl:
Eine große Zahl Zelte steht dort.
I prefer that one. Another option is:
Eine große Zahl von Zelten steht dort.
Anzahl on the other hand is outright indefinite.
Eine Anzahl Zelte steht dort.
A number of tents are set up there.
Anzahl means we don't even attempt to count them and that usually because it's a small number and someone could easily double it by counting again and find those hidden behind others.
If you know the approximate number, you could also use "Dutzende", "Hunderte", "Tausende", which would sound very natural to a German.
Hunderte Soldaten errichteten Dutzende Zelte auf der Wiese, begleitet von Tausenden Einwohnern, die sich das Spektakel nicht entgehen lassen wollten.
I'm not German so I can't say with certainty, but I think I have heard the phrase "jede Menge" many times to indicate a large amount of something. So like
Jede Menge Zelte sind aufgebaut
I think it's a very informal way of saying it, but maybe a native German here can confirm if it sounds natural.
"Eine Unmenge von Zelten" would imply a very large number. Strictly speaking, "Unmenge" is a negation of "Menge", and "eine Menge von Zelten" would mean "a lot of tents" in the usual meaning, and "a set of tents" in the mathematical meaning.
The implication of "Unmenge" is that you would not be able to count or specify it due to its size, so it is quite stronger than the comparatively lacklustre "eine Menge von Zelten".
An adjective you could employ in a similar meaning would be "unzählige Zelte" or also "unzählbare". Again, this means too large to count: if there are other reasons for an entity being not countable, you'd use "nicht zählbare" instead. Here the negations "un-" and "nicht" carry quite different connotations.
While it seems more natural to simply say zahlreiche/viele Zelte, the same is true in English: These adjectives have direct equivalents in "numerous/many", and simply saying "many tents" is a simpler and perhaps a bit less formal.
For example, I'd expect a police report about a crowd use "large number of participants", and in German "große Anzahl von Teilnehmern" instead of simply saying "many" resp. "viele".
Therefore, in order to preserve the somewhat elaborate style, I'd go with the direct translation of eine große Zahl/Anzahl von Zelten. In my opinion both word choices are equally good, and the semantic difference is minimal to nonexistent.
I want to add a little bit of detail, in the construction
Eine große Anzahl [noun]
the noun is formally in the genitive plural. this can be easily seen when you add an adjective to the noun as in
Eine große Anzahl junger Menschen
It is also visible when the noun is a nominalised adjective or participle:
Eine große Anzahl Delegierter
