Number is regularly used with count nouns <a large number of mistakes><any number of times> while amount is mainly used with mass nouns <annual amount of rainfall><a substantial amount of money>. The use of amount with count nouns has been frequently criticized; it usually occurs when the number of things is thought of as a mass or collection <glad to furnish any amount of black pebbles — New Yorker><a substantial amount of film offers — Lily Tomlin> or when money is involved <a substantial amount of loans — E. R. Black>.
Examples of AMOUNT
The drug is not being produced in adequate amounts.
What is the amount to be paid?
An amount was finally agreed upon.
The new law limits the amount a candidate can spend.
When he died we found he owed money to the amount of $250,000!