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Alphabet arrangement

by harsh.champ » Sun Feb 07, 2010 11:55 am
A five letter word having distinct alphabets is formed using the five alphabets 'C', 'O', 'I', 'W' and 'T'. All such possible five letters words are written in an alphabetical order from CIOTW to WTOIC. What will be the 60th word written?

(A)OTWIC
(B)OTCIW
(C)OIWTC
(D)OCTIW
(E)OICTW

The correct answer is C.
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by shashank.ism » Sun Feb 07, 2010 11:56 am
harsh.champ wrote:A five letter word having distinct alphabets is formed using the five alphabets 'C', 'O', 'I', 'W' and 'T'. All such possible five letters words are written in an alphabetical order from CIOTW to WTOIC. What will be the 60th word written?

(A)OTWIC
(B)OTCIW
(C)OIWTC
(D)OCTIW
(E)OICTW

The correct answer is C.
Lets start with the fixing first letter as C
so The total no. of word that can be formed with first letter as C = 4! = 4x3x2x1 = 24.
Now words with the first letter as I
so The total no. of word that can be formed with first letter as C = 4! = 4x3x2x1 = 24. Total=24+24=48.
Now we calculate with word starting with O and 2nd letter C
Total no. of word that can be formed with first 2 letter as OC = 3! =3x2x1 = 6. Total =48 +6 =54.
Now we calculate with word starting with O and 2nd letter I
Total no. of word that can be formed with first 2 letter as OI = 3! =3x2x1 = 6. Total =54 +6 =60.

ie last word which can be produced with first 2 letter as OI is the 60th one and i.e. = OIWTC
The correct answer is C.[/quote]
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by ajith » Sun Feb 07, 2010 12:28 pm
harsh.champ wrote:A five letter word having distinct alphabets is formed using the five alphabets 'C', 'O', 'I', 'W' and 'T'. All such possible five letters words are written in an alphabetical order from CIOTW to WTOIC. What will be the 60th word written?

(A)OTWIC
(B)OTCIW
(C)OIWTC
(D)OCTIW
(E)OICTW

The correct answer is C.
There are 120 word arrangements possible with five alphabets 'C', 'O', 'I', 'W' and 'T'.

in the dictionary 24 with first letter C comes first
24 with the I comes next (48)
of the 24 starting with O
6 starts with OC (54)
6 Starts with OI (60)

The last word in the dictionary starting with OI is OIWTC (60th)
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