Using adjectives to describe the word "number"

Greetings all,

I'm working with some Japanese high school teachers on some translation exercises, and we've run into a bit of a sticking point. One sentence essentially translates to "There are a lot of people who do X", but can be more directly translated as "The number of people who do X is..." My question is this - what should follow the ellipsis?

a) "The number of people who do X is many" seems incorrect because 'number' is singular, and 'many' is used for plural nouns.
b) "The number of people who do X is much" and

c) "The number of people who do X is a lot" feel very unnatural, but to my knowledge follow the necessary grammatical rules.

I suggested "The number of people who do X is great/large/high," but is there any reason why b) and c) are grammatically incorrect? Or do they merely sound that way to my ear because it isn't a common construction?

To the same effect, as a massive army pours over the castle walls, we might hear our lieutenant say "My lord, their numbers are too many." Would, "My lord, their number is too much" be equally as correct (or incorrect, if our lieutenant was wrong to say the first sentence)? Any particular reason why?

Any and all help would be most appreciated,
Cheers