A certain casino uses 10 standard decks of cards mixed toget

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.

Solution

The required combination of different 10 card hands are:

520C10*420C10*320C10*220C10*120C10*20C10.

Since first out of 520 we are choosing 10 then same 10 can exist in 10 total ways - so we eliminate 100 total cards then again select fresh 10 cards, then again we progressively reduce 100 cards and make fresh selection of 10 cards.