All the letters of the word 'MOTHER' are written in all possible ways and the strings of letters (with or without meaning) so formed are written as in a dictionary order. Then the position of the word 'THROEM' is

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642

648

646

647

answer is C.

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Detailed Solution

E,H,M,O,R,T

Number of words staring with $E = 5!$

Number of words staring with $H = 5!$

Number of words staring with $M = 5!$

Number of words staring with $O = 5!$

Number of words staring with $R = 5!$

Number of words staring with $T E = 4!$

Number of words staring with $T H E = 3!$

Number of words staring with $T H M = 3!$

Number of words staring with $T H O = 3!$

Number of words staring with $T H R E = 2!$

Number of words staring with $T H R M = 2!$

Number of words staring with $T H R O E M = 0!$

=647

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