CBSE Class 11-science Answered
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 | 21 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 | 21 Oct, 2010, 04:24: PM
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