To date, there are 11,986 unique cards released for Magic The Gathering. There are certain rules specifying constraints on deck building:
- A deck must have a minimum of 60 cards.
- A deck may not have more than four of any particular card.
(Please note that we are ignoring land cards)
I have come up with the following expression. Is it right? If so, what is its order of magnitude (wolframalpha fails to evaluate it).
$\large\large\sum_{n=60}^{47944} {47944 \choose n}$