7. Singular and plural
7.4 Partitive expressions
The expressions half of and none (of) may take either a singular or a plural verb when the noun they modify is countable. Otherwise, the verb must be singular.
None of our graduates has had / have had problems gaining a grant for further studies.
The expression the majority (of) takes a plural verb if the following noun is a collection of individuals.
The majority of our graduates have had no problem gaining a grant for further studies.
When a number (of) means several, it takes a plural verb.
A number of applications are still to come.
Meanwhile, the number (of) takes a singular verb.
The number of applications is small.