I believe the number of solutions you get should be 12-choose-3 instead of 13-choose-4. After the number of cards in each of the first three suits is chosen, the number of cards in the fourth suit is already determined.
The usual explanation for this in a standard combinatorics class use the “stars and bars” method: https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics).
Thanks! I’ve updated the post to fix this.
I believe the number of solutions you get should be 12-choose-3 instead of 13-choose-4. After the number of cards in each of the first three suits is chosen, the number of cards in the fourth suit is already determined.
The usual explanation for this in a standard combinatorics class use the “stars and bars” method: https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics).
Thanks! I’ve updated the post to fix this.