Amount, Quantity or Number?

Source: http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv129.shtml

AMOUNT
An amount of something is how much of it there is that you can measure. 
Amount is normally uncountable, so we CANNOT say: 'a large amount of cows were infected.'
But we would say:

• The amount of work I got through in July was double the amount that I did in June.
• No amount of love would heal the hatred she felt.
• I had a certain amount of respect for him: he was a good footballer and a good ambassador for his country.

We can also use amount as a verb, as in amount to, and again this describes the counting or measuring of something:

• When you added everything up, his total expenditure on this project amounted to £9,950.
• I don’t think the talks in Helsinki will amount to very mucH.

QUANTITY
Similarly, a quantity is an amount of something that you can measure or count. We often talk about large or small quantities of something. It is usually applied to inanimate objects so again it is unlikely that we would say: 'a large quantity of cows were infected'. But we would say:

• There were very small quantities of peppers on sale in the market.
• There are very large quantities of gas beneath the North Sea.

We often contrast quantity with quality:

• It doesn’t matter how many words you write: it is the quality that is important, not the quantity.
• These toys are sold in quantity and the quality doesn’t seem to matter

 NUMBER
We use number to describe how many, and often we do not know exactly how many there are. This is one of the defining aspects of a number of. Number is countable and can be applied to both animate and inanimate items, so this is the one that fits your sentence:

• a large number of cows were infected.
• There are a number of reasons why I can’t marry you.
• A number of people were injured in the explosion.
• I had warned her not to go there any number of times, but she wouldn’t listen