Hi, As a general rule, - number of + countable (plural) nouns: The number of homeless people has increased dramatically - amount of + uncountable nouns: He inherited a large amount of money . Have a look at the following usage note, though! "The traditional distinction between amount and number is that amount is used with mass or uncountable nouns ( the amount of paperwork; the amount of energy ) and number with countable nouns ( a number of songs; a number of days ).
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