(4.1.1) Difference between 'A number of' and 'The number of'

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.

3.1.1 The use of 'Just'

What are the uses of 'Just'

The word 'Just' has various uses and meanings:
(1) 'Just' is used as an adverb of time with the present perfect tense:
The bell has just rung.
Here 'just' means 'a very short time ago.'
(2) Just = Exactly
This will be just the place.
The weather is just right, not too hot, not too cold.
(3) Just = Only
Just a minute.
There is just one apple left.
(4) Just = After a short time
The train is just going to start.
(5) Just = Approximately
It is just about ten o'clock.
Some more examples -
1. Every thing happened just as you said it would.
2. I was just leaving the house when you came.
3. Surely you are not serious. You are just joking.
4. This present is just what I was wanting.
5.My grandmother is just about ninety years old.