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I wonder if the second sentence is correct.

Let "a" be the number of apples, "b" be the number of bananas, and "c" be the number of oranges.

and

Let "a" be the number of apples, "b" the number of bananas, and "c" the number of oranges.

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    Sounds okay to me. – Xanne Mar 15 '18 at 8:37
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    It's a common deletion. No problem where lack of clarity doesn't result. – Edwin Ashworth Mar 15 '18 at 10:19
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There is something called "parallelism" in English, or parallel structure. When someone wants to use similar grammatical structures in a sentence (such as, in your case, the word "be" after a subject), they would tend to eliminate unnecessary words to make it easier to clarify. Since there is already "be" in the first sentence, and it would be repeated twice more, it would make sense to get rid of "be" the next times around to make the sentence easier to read.

You might be thinking of whether "the" should also be eliminated since it, too, is repeated in each clause. This is not the case since it is describing the objects, i.e. "number of...", and omitting it would be incorrect grammar.

Here is more information about parallelism: https://www.thoughtco.com/parallelism-in-grammar-1691569

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