The little detail I reference is the use of number and amount. Number refers to items that can be counted. However, amount refers to items that cannot be counted.
This rule makes good sense. Number is a noun and a verb, and the verb form (to number) is a synonym of the verb to count. So pairing number with items that can be counted makes sense.
Amount, on the other hand, is better paired with items that cannot be counted. Whereas number implies a definite quantity that can be quoted, amount is more indefinite. The word does not imply that any definite quantity can be told. Maybe it could be learned and then told, but then again maybe not. This nebulous quality surrounding the word amount lends it to be paired more appropriately with what cannot be counted.
Consider, for instance, the example sentence in the graphic above. Even though the exact number does not appear in the sentence, lots can be counted. Thus, the appropriate word is number, not amount.