There are subtle differences between 'amount of', 'quantity of' and 'number
of'.
Amount Of
The term 'amount of' is used for things you cannot
measure (See non-countable nouns).
It usually precedes a singular word.
Examples:
I
undertook an inordinate amount of work. 
(work - singular and cannot be measured or counted)
She had a
certain amount of respect for the sales team, but she always dissented when they
spoke at meetings. 
(respect - singular and cannot be measured or counted)
It is not
difficult to see where that amount of hate derives. 
(hate - singular and cannot be measured or counted)
The amount of women in London who flirt with their own husbands is perfectly scandalous. It looks so bad. It is simply washing one's clean linen in public.
(Oscar Wilde)
(women - plural and can be counted. 'The number of women...' )
Quantity Of
The term 'quantity of' is used for things that
you can measure. (See countable nouns).
It is usually applied to inanimate objects. Some grammar references may
advocate that it can only precede a singular word; however, this view is now considered
outdated.
Examples:
I took
control of a large quantity of money.
(money - singular and can be measured or counted)
The ship
was only carrying a large quantity of mangoes.
(mangoes - plural and can be measured or counted)
('Number of' could also be used in this example. 'Number of' is preferable
as it is unlikely to be considered incorrect by some readers.)
Number Of
The term 'number of' precedes a plural, countable
noun. It can be applied to both animate and inanimate objects.
Examples:
The
disease affected a large number of camels in the town.
(camels - plural, animate and can be counted)
The ship
was only carrying a large number of mangoes.
(mangoes - plural, inanimate and can be counted)
('Quantity of' could also be used in this example.)
Select the correct version:
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LESS AND FEWER
'Amount of' should be used with a singular word, and 'number of' should be used
with a plural word. Similarly, 'less' should be used before a singular word, and
'fewer' should be used with a plural word.
See the lesson Less and fewer.
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QUANTITY OR AMOUNT
Some people may have different ideas on what is measurable. For example:
Do I need that amount of
sleep?
Is sleep measurable? If you judge that sleep can be measured in
hours, then 'quantity of sleep' could be an acceptable alternative. In
general, tangible objects (i.e., things you can touch) attract 'quantity of' and
intangible objects attract 'amount of'.
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