My Math Forum Probability of Senators From The Same State Consecutively in Alphabetical Order

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 June 14th, 2019, 06:35 PM #1 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 661 Thanks: 87 Probability of Senators From The Same State Consecutively in Alphabetical Order Of the 100 senators, the only two consecutively in alphabetical order who are from the same state are Richard (Dick) Durbin and Tammy Duckworth from Illinois. Since last in alphabetical order doesn't loop around to first, there are 99 pairs of senators consecutively in alphabetical order. Other than the first and last senator, every senator is in a pair with the senator before him or her and the senator after him or her. Is it possible to calculate the probability of 0, 1, 2, etc. (until the probability gets tiny) states having their senators consecutively in alphabetical order without giant numbers? For example, 100!/(2^50) with the denominator being because the two senators from each state are identical (for this purpose, not the same person) is giant.
 June 14th, 2019, 09:13 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2216 In alphabetical order of full name or what?
 June 15th, 2019, 04:26 AM #3 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 661 Thanks: 87 By last name with first name after that if necessary. Rick Scott and Tim Scott are the only ones with the same last name, and Rick goes first. Alphabetical order and another method like age order would produce the same probabilities as long as there are no ties, which there aren't.

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