- A plethora of problems
- Plethora of problems
Are both ok? Because in many articles, "A" is not written.
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No, you must use the article — and under most circumstances, the indefinite one. That’s because this is simply how such premodifying phrases used as noun quantifiers are always constructed. They must all follow this formula:
a(n) + NOUN (singular) + of + NOUN (either singular or plural)
It no more makes sense to use plethora of X without an indefinite article preceding it than it does any of these formulations:
Those all mean something rather like the quantifier many (or too many) if it’s a plural noun following, and something rather like the quantifier much (or too much) if it’s a mass noun following.
Please be aware that those examples are taken from a wide variety of registers. They are therefore not meant to be identical to the point of all being freely interchangeable within the same work. Some are common, others are rare.
Occasionally these can take a definite article when the sense requires it, as in
The resulting surfeit of entrants overwhelmed their sign-up desk.
Be advised that words like plethora and surfeit are “fancy” ones that belong to a far higher register than one normally employs in casual communications.