IIT JEE , AIEEE Forum - Mathematics , Algebra - permutation problem

viswanath

All the letters of the word AGAIN are permuted in all possible ways and the word so formed with or without meaning are written as in dictionary ( in alphabetical order). Then what is the 50th word?

akhil_o

edited....see below

its NAAIG

viswanath

nope.

akhil_o

It can be easily solved by arranging the first 2 letters in alphabetical order...the

rest 3 adjust themselves accordingly

here is the list of words according to preference:

AA ( GIN)-----------------6 words

AG ( AIN)-----------------6 words

AI (AGN)----------------6 words

AN (AGI)-----------------6 words

GA (AIN)-----------------6 words

GI (AAN)---------------3 words

GN (AAI)-----------------3 words

IA (GAN)---------------6 words

IG (AAN)---------------3 words

IN (AAG)---------------3 words

NA (AGI)

...

... and so on

now we can see that by the end of IN(AAG) we complete 48 words

so the 50th word will be second word of next row

1st-NAAGI, second- NAAIG

so we hav 50th word NAAIG

chimanshu_007

AAGIN

4! ways that the word starts frm A....

4!/2! ways that it can be started by G

4!/2! ways that it can be started by I

total

24 + 12 + 12 = 48......

2 words left....

it must start with N

49th word is NAAGI , 50th IS NAAIG.......

prateek2292

The answer is NAAIG.
the words are
A,A,G,I,N.
no. of words starting from A are 4!=24.
no. of words starting from G are 4!/2!=12.
no. of words starting from I are 4!/2!=12
Therefore total no. of words are 48.
Therefore also next 12 words are from N.
That means 50th word starts from N.
For the second place we first consider A which have 3! of words.
that means at second's place it is A.
At third position we have first consider A.
A have 2 words from it.
Therefore the word till now is " NAA".
After that it is G & I to go.
according to dictionary G will come first than I.
Therefore NAAGI is 49 th word.
And "NAAIG" is the 50 th word.

pantpranav

The word would be NAAIG.

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