What is the difference between 'A number of---' and 'The number of ---'
'A number of'' means 'many'.'The number of' means 'a single figure'
"A number of ---" is treated as a plural subject so it takes a plural verb:
A number of books are lying on the floor.
A number of boys have already come here.
A number of students have got good marks in English.
A number of girls are absent today.
"The number of ----" is treated as a singular subject so it takes a singular verb:
The number of girls in the class is twenty.
The number of books missing is not known.