2002 AMC 10B Problem 6

Factor as $n^2 - 3n + 2 = (n-1)(n-2).$ For $n \ge 4,$ both factors exceed $1,$ so the product is composite. For $n = 1$ and $n = 2$ the value is $0,$ and for $n = 3$ the value is $(2)(1) = 2,$ which is prime. So exactly one value of $n$ works. Thus, the correct answer is B.