MHB Rank & Letter of $\bf{\mathbb{INDONESIA}}$ in Dictionary

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The discussion focuses on determining the rank of the word "INDONESIA" when all its letters are arranged alphabetically in an English dictionary. It also explores identifying the 61st letter in the dictionary sequence formed by these letters. The conversation references a blog post by Surya that provides insights on calculating the rank of a word with repeated letters. Participants engage in calculations and reasoning to arrive at the correct rank and letter position. Overall, the thread emphasizes the mathematical approach to word arrangement and ranking.
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If all the letters of the world $\bf{\mathbb{INDONESIA}}$ are arrange in a English Dictonary, Then

$(a)\;\; $ Rank of The word $\bf{\mathbb{INDONESIA}}$

$(b)\;\; 61^{th}$ Letter in Dictonary araanging $\bf{\mathbb{INDONESIA}}$
 
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There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...

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