grammaticality - A number of questions "has been" or "have been" asked?

Formally, is it correct to write:

A number of questions has been asked here.

or:

A number of questions have been asked here.

As a non-native speaker of English, I would prefer the former: the subject seems to be "number", therefore the verb ought to be singular, I'd say. However, the latter seems more common, and therefore I believe that my gut feeling is just plain wrong — but I would really like to have a definite answer.

Moreover, is it the same for "a myriad of", "a plethora of", and so on?

Answer

"The number" is singular. "A number", however, is plural, and takes a plural verb. Thus, for both informal and formal usage, the following is correct:

A number of questions have been asked here.

See the usage note not quite halfway down the page at Dictionary.com, or this daily writing tip.