Latest m4maths Aptitude Question SOLUTION: . Rank of the word DEHRADUN in the dictionary of words formed by letters of the word DEHRADUN taking all letters at a time?

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(#M40011648) M4MATHS question Keep an EYE

. Rank of the word DEHRADUN in the dictionary of words formed by letters of the word DEHRADUN taking all letters at a time?

Asked In m4maths PARAG KAMRA (11 years ago)

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Balakrishnan M  (11 years ago)

Starting from "A" can form the word =(7!/2!)ways
Starting from"DA" can form the word = 6! ways
Starting from "DD" can form the word = 6! ways
Starting from "DEA" can form the word = 5! ways
Starting from "DED" can form the word = 5! ways
Starting from "DEHA" can form the word = 4! ways
Starting from "DEHD" can form the word = 4! ways
Starting from "DEHN" can form the word = 4! ways
Starting from "DEHRADN" can form the word =1!ways
The word "DEHRADUN" is = 1
The Rank of the word = (7!/2!)+6!+6!+5!+5!+4!+4!+4!+1!+1
= 2520+720+720+120+120+24+24+24+1+1
= 4274

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Pallab Roy Chowdhury  (11 years ago)

Write the alphabetical order of the letters of the given word 'DEHRADUN' as A,D,D,E,H,N,R,U.
Now strike off the first letter D.
Then count the no.of letters before D, and it is equal to 1(A).
So,number of words starting with A=1*(7!/2!)[since,there are 2 D's in the remaining 7 letters]
Now strike off the next letter E.
Then count the no.of letters before E, and it is equal to 2(A & D).
So,number of words starting with DA=(6!/1!).
So,number of words starting with DA=(6!/1!).
Now strike off the next letter H.
Then count the no.of letters before H, and it is equal to 2(A & D).
So,number of words starting with DEA=(5!/1!).
So,number of words starting with DED=(5!/1!).
Likewise,number of words starting with DEHA=(4!/1!).
number of words starting with DEHD=(4!/1!).
number of words starting with DEHN=(4!/1!)
number of words starting with DEHRADN=(1!/1!)
Hence,we the requred rank will be=
(1*(7!/2!))+(2*(6!/1!))+(2*(5!/1!))+(3*(4!/1!))+(0*(3!/1!))+(0*(2!/1!))+(1*(1!/1!))+(0*(0!/1!))+1=
2520+1440+240+72+0+0+1+0+1=4274.

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AKANKSHA SINGH  (11 years ago)

ans) 6794......
wrd strtng frm A=7!=5040
wrd strtng with DA=6!=720
wrd strtng with DD=6!=720
wrd strtng with DEA=5!=120
Wrd strtng with DED=5!=120
wrd strtng with DEHA=4!=24
wrd strtng with DEHD=4!=24
wrd strtng with DEHN=4!=24
after this wrd will be DEHRADNU....next wrd will b DEHRADUN
SO, ans=5040+720+720+120+120+24+24+24+2=6794

Is this solution Helpfull? Yes (1) | No (4)  

Pallab Roy Chowdhury  (11 years ago)

Write the alphabetical order of the letters of the given word 'DEHRADUN' as A,D,D,E,H,N,R,U.
Now strike off the first letter D.
Then count the no.of letters before D, and it is equal to 1(A).
So,number of words starting with A=(7!/2!)[since,there are 2 D's in the remaining 7 letters]
Now strike off the next letter E.
Then count the no.of letters before E, and it is equal to 2(A & D).
So,number of words starting with DA=(6!/1!).
So,number of words starting with DD=(6!/1!).
Now strike off the next letter H.
Then count the no.of letters before H, and it is equal to 2(A & D).
So,number of words starting with DEA=(5!/1!).
So,number of words starting with DED=(5!/1!).
Likewise,number of words starting with DEHA=(4!/1!).
number of words starting with DEHD=(4!/1!).
number of words starting with DEHN=(4!/1!)
number of words starting with DEHRADN=(1!/1!)
Hence,we the requred rank will be=
(1*(7!/2!))+(2*(6!/1!))+(2*(5!/1!))+(3*(4!/1!))+(0*(3!/1!))+(0*(2!/1!))+(1*(1!/1!))+(0*(0!/1!))+1=
2520+1440+240+72+0+0+1+0+1=4274.

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