Suppose we have a pack of $52$ cards. Each card has a number from $1$ to $13$ and there are $4$ identical cards for each number. We are searching for the number of the different ways we can put those $52$ cards in a row.
Is the answer $ \cfrac{52!}{(4!)^{13}} $ correct ?
My reasoning was that for every quartet of the same number, there are $ 4! $ ways of ordering (assuming that the elements were different), so for $ 13 $ quartets, we would have to divide $ 52! $ (which would be the answer if all cards where different) by $ (4!)^{13} $.
Thanks in advance