Combinatorics: Number of possible 10-card hands from superdeck (10 times 52 cards) I have the following problem from book "Introduction to Probability", p.32

A certain casino uses 10 standard decks of cards mixed together into one big deck, which
  we will call a superdeck. Thus, the superdeck has 52 · 10 = 520 cards, with 10 copies
  of each card. How many different 10-card hands can be dealt from the superdeck? The
  order of the cards does not matter, nor does it matter which of the original 10 decks
  the cards came from. Express your answer as a binomial coefficient.
  Hint: Bose-Einstein.

My solution:
Because the number of cards of each type in the superdeck (10) is not less than the size of the hand (10), and thus not limiting, it's the same as sampling with replacement where the order does not matter, 
so the number of possible 10-card hands would be $\binom{52+10-1}{10}$.
Is my thinking correct?

I think your answer is correct but your thinking is half way there.
Consider n=10 number of copies are indistinguish stars, and k=52 is distinguish bins.
If we just simply follow the Bose-Einstein(sampling with replacement and order doesn't matter), we would have $\dbinom{10+52-1}{52}$ or $\dbinom{10+52-1}{9}$
Since we are not putting 10 copies into 52 bins, it is more clear to me to think in this way $:\\$
Consider n=10 number of copies are indistinguish stars, and k=52 is distinguish bins(easier to imagine if you associate it with the idea of the degree of freedom). Then there are $10+52-1$ locations/bins for us to choose from, each location/bin contains 1 card, and we want 10 cards hand, then the solution becomes $\dbinom{10+52-1}{10}$
