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 · 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.

Answer 1

(₁₀⁶¹)

Explanation:

In order to select 'm' item from a given set of 'n' items, the binomial coefficient is commonly used. In this problem, there are card with numbers from 1 ... 52, if we have 'i' type of cards with the total number of
`x_(i)`. Then:

`x_(i)` ∈ positive real numbers

0 ≤
`x_(i)` ≤ 10

Therefore, if we use the Bose-Einstein theorem, the different methods of dealing with the cards are:

(₁₀⁵²⁺¹⁰⁻¹) = (₁₀⁶¹)