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The letter of the word MOTHER are arranged in all possible ways and the resulting words are arranged as in dictionary. If the rank of the word is K, then the number of positive integral divisors of k is

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answer is 4.

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Detailed Solution

Given word is MOTHER

Alphabetical order of the word MOTHER is E,H,M,O,R,T

Rank= 2(5!)+2(4!)+3(3!)+0(2!)+1=309

$\Rightarrow 309 = 3 \times 103 N u m b e r o f d i v i s o r s = 2 (2) = 4$

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