# the letter of the word mathematics are written in all possible orders and these words are written out as in dictionary find the rank of mathematics

SHAIK AASIF AHAMED
7 years ago
Given a word all the letters of it are permuted in all possible ways and thus formed words are arranged as in a dictionary. Then the position of the given word is simply called rank of the word.

Procedureto find the rank of a word
Step 1: Write the word and above it,put the alphabetical ordering.
Step 2:Write below,the factorial values starting with 0!(=1) from right to left.
Step 3:Write the number of numbers less than(in top row) the number towards right of it.
Step 5:Add "1" to get the rank of the word.
The rank of the word "MATHEMATICS" is
Step 1: 6 1 8 4 3 6 1 8 5 2 7
M A T H E M A T I C S
Step 2: 10! 9! 8! 7! 6! 5! 4! 3! 2! 1! 0!
Step 3: 6 0 7 3 2 3 0 3 1 0 0
Step 4: MULTIPLYING values obtained in step 2 and 3 like 6*10!+1*9!+....

we get 22071980
Step 5: 22071980+1=22071981

Therefore 22071981is the rank of the word "MATHEMATICS"

Thanks and Regards
Shaik Aasif
Sumit Majumdar IIT Delhi
7 years ago
1. Dear student,
Let me explain a similar case for Mother, you may attempt the same for Mathematics.
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.
Regards
Sumit