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Problem 987

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Straight Eight

In Poker a straight is exactly five cards of sequential rank NOT all of the same suit.
In this problem an ace can rank either high as in A-K-Q-J-10 or low as in 5-4-3-2-A, but cannot simultaneously rank both high and low, so Q-K-A-2-3 is not allowed.

There are $10200$ ways of choosing a straight from a normal $52$ card deck.

There are $31832952$ ways of choosing two disjoint straights from a single $52$ card deck.

Find the number of ways of choosing eight disjoint straights from a single $52$ card deck.

In this the order of choosing the straights does not matter.

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八手顺子

在扑克牌中，顺子指五张点数连续且花色不完全相同的牌。在本题中，A既可以作为最大牌出现在A-K-Q-J-10中，也可以作为最小牌出现在5-4-3-2-A中，但不能同时充当最大牌和最小牌，因此Q-K-A-2-3是不合法的。

从一副标准的$52$张扑克牌中选出一手顺子，共有$10200$种方式。

从一副标准的$52$张扑克牌中选出两手顺子（不能用相同的牌），共有$31832952$种方式。

求从一副标准的$52$张扑克牌中选出八手顺子（不能用相同的牌）的方式数目。

注意本题中选取各手顺子时不计先后顺序。

译注：本题标题还可以直译为直列八缸（发动机），可能是双关语梗，但这也太难翻了……

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