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Question

The letters of word OUGHT are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word TOUGH is

A
89
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B
90
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C
91
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D
92
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Solution

The correct option is A 89
Letters present in the word OUGHT are O,U,G,H,T.
Order of the letters according to the alphabet is G,H,O,T,U.
Number of words starting with G (G _ _ _ _) is 4!.
Number of words starting with H (H _ _ _ _) is 4!.
Number of words starting with O (O _ _ _ _) is 4!.
Number of words starting with TG (TG _ _ _) is 3!.
Number of words starting with TH (TH _ _ _) is 3!.
Number of words starting with TOG (TOG _ _) is 2!.
Number of words starting with TOH (TOH _ _) is 2!.
Then the next word will be TOUGH.

The rank of the word TOUGH
=4!+4!+4!+3!+3!+2!+2!+1=89

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