Permutations with repetition and size constraint

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Suppose you are given the digits 1, 1, 2, 2, 3, 3, 4, 4. How would you find the number of 3-digit permutations you can create from those?

For 8-digit permutations the answer should be $\frac{8!}{2!2!2!2!}$ I believe.

However, I cannot think of a way to do this when asked for permutations where not all of the set is used. I have tried $\frac{8P3}{2!2!2!2!}$ but that does not match the amount when I try manually listing all permutations which seems to be 60.

If the problem were to be generalized what would a solution look like?

Thanks in advance.