Exercise 1.13

Question

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  \cdot  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.

fifthist x · Accepted Answer

The problem amounts to sampling with replacement where order does not matter, 
since having $10$ copies of each card amounts to replacing the card. 
This is done using the Bose-Einstein method.

Thus, the answer is $${52 + 10 - 1 \choose 10} = {61 \choose 10}$$

Exercise 1.13

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Exercise 1.13

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