SOLUTION: if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the rank of the word 'MOTHER'.

Question 350590: if the letters of the word 'MOTHER'are written in all possible order and these words are written out as in dictionary ,find the rank of the word 'MOTHER'.
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
The letters of the word WOMAN are written in all possible orders and these words are... (answered by edjones)

The letters of the word WOMAN are written in all possible orders and these words are... (answered by richard1234)

The letters of the word ZENITH are written in all possible orders.How many words are... (answered by ewatrrr)

a dictionary is printed consisting of 7 letters words CRICKET. If the word are printed at (answered by ewatrrr,Lubi001)

1) If all permutations of the letters of the words AGAIN are arranged as in... (answered by jim_thompson5910)

if all permutations of the letters of the word AGAIN are arranged as in dictionary,then... (answered by ikleyn,greenestamps)

A child forms three-letter "words" using three different letters from HISTORY. A... (answered by ikleyn,greenestamps)

How many words can be written using all the letters of the word... (answered by ikleyn)

Using only letters from the set {A, M, T, N, Y, S}, all of the possible four-letter... (answered by scott8148)