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The letters of the word REGAIN when arranged as per dictianory, find the 32nd word.

a)AEGIRN

b)AEGRIN

c)AEIGRN

d)none of these

MyApproach

As per dictionary order, alphabets will follow the order AEGINR.

Now,Starting with A,other letters will have 5! ways to form i.e $120$.Hence 32 word will not be there.

Starting with AE letters will have $24$ letters....1

Staring with AGE letters will have $6$ letters.....2

But I am confused how to follow the Ans from here. Can anyone guide me how to follow this approach?

justin takro
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    So from what you have written ..you are saying that number of words starting with $AE$ will be equal to $24 (4×3×2×1)$ and we are required to find 32nd word ..so as all the words given in option start with $AE$ and as $24<32$ so whatever the 32nd word will be it will surely not start with $AE$ but all the options given here start with $AE$ ....so naturally one answer is left!!...you can Also specifically calculate 32nd word...but since it was a multiple choice question...so i don't think there is a problem with this... – Freelancer Nov 17 '15 at 16:53
  • I think you were close to a correct analysis. The first $4!=24$ words begin with AE. So the $32$-nd word cannot begin with AE. – André Nicolas Nov 17 '15 at 16:54
  • @AndréNicolas AGE will have letters till 30 Its 30 letter will be AGERNI Am i right?. 31 and 32 will be AGIENR.32 word will be AGIERN – justin takro Nov 17 '15 at 17:10
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    Yes, the next $3!$ after the words that begin with AE start with AGE. And then you got the next two right, so you correctly found word $32$. But this was not necessary to answer the multiple choice question. – André Nicolas Nov 17 '15 at 17:18

1 Answers1

2

Seems it's AGIERN so the correct answer is "none of these".

AEGxxx -> 6

AEIxxx -> 6

AENxxx -> 6

AERxxx -> 6

AGExxx -> 6

and then the next two are:

AGIENR
AGIERN

So the answer is AGIERN.

peter.petrov
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