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'.
Answers
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
There are 6 letters and all are different.
In dictionary, words starting from E, H will come before word MOTHER.
so, total no. of words starting from E = 5!= 120
(we have to arrange 5 letters on five places)
similarly, no. of words starting from H = 5! = 120
now, first word starting with letter M will come..
similarly, no. of words starting with ME.... = 4!
no. of words starting with MH.... = 4!
now, words starting from MO will come
no. of words starting with MOE... =3!
no. of words starting with MOH... =3!
no. of words starting with MOR... =3!
now, words starting from MOT will come
no. of words starting with MOTE.. = 2!
then after words starting from MOTH will come and first word will MOTHER
so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3!
= 120 +120 + 48 + 18
= 306
so, rank of MOTHER in dictionary = 307
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