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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

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

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2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 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 4:Multiplythe numbersshown byand add.
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
askIITians Faculty
Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
6 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

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