Problem 369

Badugi

In a standard 52 card deck of playing cards, a set of 4 cards is a **Badugi** if it contains 4 cards with no pairs and no two cards of the same suit.

Let f(`n`) be the number of ways to choose `n`
cards with a 4 card subset that is a Badugi. For example, there are
2598960 ways to choose five cards from a standard 52 card deck, of which
514800 contain a 4 card subset that is a Badugi, so f(5) = 514800.

Find f(`n`) for 4 `n` 13.

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