Rank of the word DEHRADUN in the dictionary of words formed by letters of the word DEHRADUN taking a

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.

((1*7!)/2!)+((2*6!)/1!)+((2*5!)/1!)+((3*4!)/1!)+(0*3!)+(0*2!)+(1*1!)+(0*0!)+1
= 2520+1440+240+72+0+0+1+0+1
=4274

Given word is "DEHRADUN"
Now writing the word in the alphabetic order="ADDEHNRU".....(1)

Taking first letter of "DEHRADUN" is D,

D is not the first letter in eq 1 hence no of words formed from it=7!/2!=2520....(2)
Checking second word of eq (1) is D we require it
hence place it in the position,

Taking 2nd letter of "DEHRADUN" is E
Is E is the first letter of “ADEHNRU” no, Hence no of words formed from it=6!=720….(3)
Is E is the 2nd letter of “ADEHNRU” no, Hence no of words formed from it=6!=720….(4)
Since E is the 3rd letter so place it .
Now word is “ADHNRU”
Next word of “DEHRADUN” is H,
Is H is the first letter of “ADHNRU” no, Hence no of words formed=5!=120….(5)
Is H is the 2nd letter of “ADHNRU” no, Hence no of words formed=5!=120….(6)
Since H is next letter so place it.
Now word is “ADNRU”
Is “R” is the first letter of “ADNRU” no, Hence no of words formed=4!=24….(7)
Is “R” is the 2nd letter of “ADHNRU” no, Hence no of words formed=4!=24….(8)
Is “R” is the 3rd letter of “ADHNRU” no, Hence no of words formed=4!=24….(9)
Since R is the next word so place it,
Now word is “ADNU”
Since “A” is the next word so place it,
Now word is “DNU”
Since “D” is the next word so place it,
Now word is “NU”
Since “N” is not the next word, So no of words formed=2!=2……(10)
Hence total no of words are=2520+720+720+120+120+24+24+24+2=4274

total letters in "DEHRADUN"=8, D-2
word starting from 'A'- 7!/2!=7*6*5*4*3=2520
word starting from 'DA'-6!=720
word starting from 'DD'-6!=720
word starting from 'DEA'-5!=120
word starting from 'DED'-5!=120
word starting from 'DEHA'-4!=24
word starting from 'DEHD'-4!=24
word starting from 'DEHN'-4!=24
word starting from 'DEHRAD'-2!=2
hence the rank of "DEHRADUN" in dictionary=2520+720+720+120+120+24+24+24+2=4274
so answer is (5)4274

Starting with "A" can form the word =(7!/2!)ways
Starting with "DA" can form the word = 6! ways
Starting with "DD" can form the word = 6! ways
Starting with "DEA" can form the word = 5! ways
Starting with "DED" can form the word = 5! ways
Starting with "DEHA" can form the word = 4! ways
Starting with "DEHD" can form the word = 4! ways Starting with "DEHN" can form the word = 4! ways Starting with "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

(7!/2)+6!+6!+5!+5!+4!+4!+4!+2=4274