How do we use invariable plurals?

Question

I'm trying to get my head round how we use so called invariable plurals. I have been through about a million different sites now, and come up with the following:

(i) There are three main groups of invariable plurals, namely

a) nouns denoting things (typically garments and tools) that consist of two or several conjoined parts, such as scissors, trousers, binoculars, tweezers etc

b) nouns denoting groups of living beings, such as police, people, cattle, vermin, personnel, clergy etc

c) miscellaneous nouns ending in -s, such as arms, fireworks, belongings, oats, valuables, regards, remains, clothes etc

(ii) All three kinds of invariable plural always take plural verb form (the binoculars were very expensive), always take plural demonstratives (these binoculars are expensive) and are always replaced by plural, rather than singular anaphoric pronouns (Did you see those binoculars? They were very expensive)

Now to my questions:

Have I got things right so far? If not – where did I go wrong?
Apart from impact on choices of verb form, demonstratives and anaphors, I'd also like to know whether invariable plurals are all countable (only there can never be just one) – that is, can we use cardinals (except one) and quantifiers that normally go only with countables (e.g. many and several) with all of them? If not, can we distinguish any kind of pattern? 
Is group (b) above distinct from what's generally referred to as collective nouns, or is it the same? If it's not the same, how do we tell them apart?

Thank you!

James K · Answer

The treatment with a cardinals differes between the groups:
In the first type, we use "a pair of"  So we say "three pairs of binoculars".  It is considered an error by some to say "three binoculars", however this usage is not uncommon when speaking quickly and casually.
"Clothes" and "clergy" can also be used as "pieces of clothing" and "members of the clergy".
Of the second type, there is often a corresponding singular word or phrase:

There are five police officers and three cows and two vicars.

Other words function as normal countable plurals

There were seven people who had shot four game-animals

"Vermin", I'd place in the third group, which function more like uncountable nouns:
In this group "oats" is like "rice".  You might say "bowls of oats", but you'd also say "how much oats", similarly "vermin"
"Firework" is not in this category, it is a normal singular noun.

He was holding a firework / two fireworks.

"Remains" could be counted, but you'd normally specify "two human remains", and "regards" only really appears in the idiom "give my regards" You couldn't put a number on it.
Words like "clergy" and "police" that seem singualar but are treated as plural are called "collective nouns" in some grammar works.

LawrenceC · Answer

I'd also like to know whether invariable plurals are all countable

Yes.  This is resolved in English through the use of the phrase pair of:

I have three pairs of binoculars.
  
  How many pairs of scissors do you have?
  
  She took three pairs of my pants.

Is group (b) above distinct from what's generally referred to as collective nouns

Yes.  If you can say X is a member of Y, then Y is a collective noun.  You can't do this nonfiguratively with invariable plurals.

How do we use invariable plurals?

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