It can represent anything. When stating a specific problem, you should clarify what each variable represents.
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The answer to this question depends what a(n) is meant to represent.
It can represent anything you want it to. The conventional use is that it represents the number of successes.
A variable is assigned to represent an unknown quantity.
Variable: A letter or symbol used to represent a number or quantities that vary
n is a variable. It could mean any number you want it to. Most of the time, it is not specified what it is. Sometimes they give you clues about it, like "5 times n is 5." In this case n is 1.