MathDB

There is a standard deck of

52

cards without jokers. The deck consists of four suits(diamond, club, heart, spade) which include thirteen cards in each. For each suit, all thirteen cards are ranked from “

2

” to “

A

” (i.e.

2, 3,\ldots , Q, K, A

). A pair of cards is called a “straight flush” if these two cards belong to the same suit and their ranks are adjacent. Additionally, "

A

" and "

2

" are considered to be adjacent (i.e. "A" is also considered as "

1

"). For example, spade

A

and spade

2

form a “straight flush”; diamond

10

and diamond

Q

are not a “straight flush” pair. Determine how many ways of picking thirteen cards out of the deck such that all ranks are included but no “straight flush” exists in them.

Problem Statement