Alright, so here goes, I'm trying to figure out all possible combinations for a $60$ card deck.
For any who wish to know, the cards in question are Magic: the Gathering. (I'll avoid the use of jargon for those who don't know what it is)
Right then. So, a standard deck of cards has $60$ cards, divided into two portions Played cards and Land cards (Land cards are used to play the played cards) There are usually anywhere from $20$ to $24$ land cards, and by extension $36$ to $40$ played cards. There can be no more than $4$ of any type of card in the deck, except for $12$, two played cards (which are omitted) and $10$ "basic" lands, these can have any number in any deck.
We'll start off with one of the more common of the bunch, $36$ to $24$.
Now, we know there are $13,707$ possible played cards and $470$ possible land cards (which aren't "basic") and $10$ possible "basic" lands.
There can be up to $4$ of any card, so for this instance, there can be anywhere from $36$ to $9$ different played cards and anywhere from $1$ to $24$ different land cards.
From here, I'm a bit confused, I believe Integrals play a part here, And I hope this is enough information to solve it.