if letters of word 'MOTHER' are written in all possible orders and these words are written out as in dictionary find the rank pof the word 'MOTHER'.

The given word is MOTHER. In a dictionary, the words are arranged in alphabetical order. The words beginning with E, H, M, O, R and T are written in order.

Number of words starting with E = 5! = 120

Number of words starting with H = 5! = 120

Number of words starting with M = 5! = 120, but one of these words is MOTHER.

Now, number of words with ME = 4! = 24

Number of words with MH = 4! = 24

Number of words with MO = 4! = 24, but one of these words is MOTHER.

Now, number of words with  MOE = 3! = 6

Number of words with MOH = 3! = 6

Number of words with MOR = 3! = 6

Number of words with MOT = 3! = 6, but one of these words is MOTHER.

The first word beginning with MOT is MOTEHR. The second word is MOTERH. The third word is MOTHER.

Therefore, rank of MOTHER = 2(120) + 2(24) + 3(6) + 3 

 = 309

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