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A problem for someone who has \(g_{64}\) free time

How many ways are there to obtain at least one straight flush with 13 cards?

I've been searching for an answer for this curious inquiry, but to no avail. I've also tried solving using inclusion-exclusion, but it has more cases than the number of possible straight flushes. Can someone solve this using some technique, or find an answer using Google? I've tried everything, but to no avail.

An olympiad approach would make an exciting problem. Inclusion-exclusion is veeery very long. Google - I've tried. But maybe you'll have better luck than me?

Clarification: Having a straight flush means having at least five cards with consecutive ranks and the same suit from a standard deck of cards.

Note by Manuel Kahayon
9 months, 2 weeks ago

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\(\infty\) Manuel Kahayon · 9 months ago

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