Hey folks, I believe this is the correct thread for this topic. I was debating between general mathematics and statistics. I believe it falls here.(adsbygoogle = window.adsbygoogle || []).push({});

So, I play the card game Magic: The Gathering, and one of the core tenants of the game is building a deck from a large variety of cards. The deck is then randomized (shuffled) and the actual game involves doing your best with the cards you've drawn, as well as knowing what you are likely to draw (reminiscent of poker.) Interestingly, in building a deck, knowledge of statistics is very useful as some cards you may want to see more than others.

One thing I've always been curious of, though, is how many possible decks can be created. It would seem like a simple combination problem, or even Combination with Repetition, except for a problem. Most cards you may have no more than four of in your deck, but there are five cards that you may have any number of in your deck.

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So, here's the question:

A deck consists of 60 cards.

There are 1729 cards of which you may have 0 to 4 copies each in your deck.

There are 5 cards of which you may have any number of copies in your deck.

How many unique decks can be built?

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More than the answer (though I'd be excited to see it,) I'd like to know how to frame an equation that would handle a situation like this. Any thoughts are welcome!

Thanks!

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# Combinations with Irregular Repetition

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