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Solution: We are asked to count the number of distinct ways to assign 10 independently classified images into 4 categories with fixed counts: 3 as tumor, 2 as inflammation, 4 as normal, and 1 as stroke. This is a multinomial coefficient problem.
The number of such classification outcomes is given by:
\frac{10!}{3! \cdot 2! \cdot 4! \cdot 1!}
We compute step-by-step:
$10! = 3628800$
$3! = 6$, $2! = 2$, $4! = 24$, $1! = 1$
Denominator: $6 \cdot 2 \cdot 24 \cdot 1 = 288$
\frac{3628800}{288} = 12600
Thus, the number of possible classification outcomes is:
\boxed{12600}