If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?

Asked by aruni_maiyer | 21st Oct, 2010, 02:12: PM

Expert Answer:

Dear student,
Given : word EXAMINATION
number of letters = 11
 
the dictionary words  before starting letter E will be starting with A
 
Case(1) first letter A and second letter also A
remaining 9 letters have two I and two N
so these are permutations with repetition,
so number of ways = 9!/(2!2!) = 9!/4
 
Case(1) first letter A and second letter also I
remaining 9 letters have two N
so these are permutations with repetition,
so number of ways = 9!/(2!) = 9!/2
 
Case(3) first letter A and second letter is N
remaining 9 letters have two I
so these are permutations with repetition,
so number of ways = 9!/(2!) = 9!/2
 
Case(4) first letter A and second letter is any of the 5 letters E, M, T, O, X
these 5 letters can be chosen in 5 ways
remaining 9 letters have two I and two N
so these are permutations with repetition,
so number of ways = 9!/(2!2!) = 5(9!/4)
 
The total number of ways from all the 4 cases
= (9!/4) + (9!/2) + (9!/2) + 5(9!/4)
= 9!(1/4 + 1/2 + 1/2 + 5/4)
=9! (5/2)
 
We hope that clarifies your query,
regards,
Team Topper Learning.

Answered by  | 21st Oct, 2010, 04:24: PM

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