Rank of the word SUBJECT in the dictionary of words formed by using the letters of the word SUBJECT

words starting with B ..= 6!= 720
words starting with C ..= 6!= 720
words starting with E ..= 6!= 720
words starting with J ..= 6!= 720
words starting with SB ..= 5!= 120
words starting with SC ..= 5!= 120
words starting with SE ..= 5!= 120
words starting with SJ ..= 5!= 120
words starting with ST ..= 5!= 120
words starting with SUBC ..= 3!= 6
words starting with SUBE ..= 3!= 6
words starting with SUBJC ..= 2!= 2
Next word is SUBJECT ..............1

so Rank of word SUBJECT = 3495 ..option 3

SUBJECT
Mark letters in ALPHABETICAL order
5714326
SUBJECT

write no of letters with lower alphabetical oder on right side of each letter
5714326
SUBJECT
4502100
write no of letters from 0 to 1 starting from right side.
5714326
SUBJECT
4502100
6543210

Hence rank = 4*6! + 5*5! +0*4! + 2*3! +1*2! +0*1!+0*0! +1 = 3495 .. option 3

No of words starting with B = 6!= 720
no of words starting with C = 6!= 720
no of words begining with E = 6!= 720
no of words starting with J = 6!= 720
no of words beginning with SB = 5!= 120
no of words starting with SC = 5!= 120
no. of words starting with SE = 5!= 120
no. of words starting with SJ = 5!= 120
no of words begining with ST = 5!= 120
no of words starting with SUBC= 3!= 6
words starting with SUBE = 3!= 6
words starting with SUBJC = 2!= 2
one rank for next word SUBJECT ..............1

Rank of word 'SUBJECT' = 3495

Formula is P(n-1)!+.....+P(n-n)!
Here n is count of the Letters
P is the position of the letters as per Alphabets

Re arrange SUBJECT word by alphabets order B C E J S T U.
Before letter S there are 4 letters (i.e. 4*6!)--1
S stricked off. Remaining letters are B C E J T U
Before letter U there are 5 letters (i.e. 5*5!)--2
U stricked off. Remaining letters are B C E J T
Before letter B there are 0 letters (i.e. 0*4!)--3
B stricked off. Remaining letters are C E J T
Before letter J there are 2 letters (i.e. 2*3!)--4
J stricked off. Remaining letters are C E T
Before letter E there is 1 letter (i.e. 1*2!)--5
E stricked off. Remaining letters are C T
Before letter C there is no letter (i.e. 0*1!)--5
and same for T as well.

Finally the the word itself will have one rank.
So 4*(6!)+5*(5!) + 0*(4!) +2*(3!)+1*(2!)+0*(1!)+1 would be the total rank (i.e.3495)

letter of the word SUBJECT in dictionary order
B,C,E,J,S,T,U
B - - - - - - ... 6!
C - - - - - - ... 6!
E - - - - - - ... 6!
J - - - - - - ... 6!
S B - - - - - ... 5!
S C - - - - - ... 5!
S E - - - - - ... 5!
S J - - - - - ... 5!
S T - - - - - ... 5!
S U B C - - - ... 3!
S U B E - - - ... 3!
S U B J C - - ... 2!
S U B J E C T ... 1!
=4*6!+5*5!+2*3!+1*1!
=2880+600+12+2+1
=3495

Arrange the word 'SUBJECT' in alphabetical order.

b c e j s t u

Now compare the letters one by one which is match the word 'SUBJECT'.

b -> 6!=720
c -> 6!=720
e -> 6!=720
j -> 6!=720
[s].b ->5!=120
[s].c ->5!=120
[s].e ->5!=120
[s].j ->5!=120
[s].t ->5!=120
[su][b].c ->3!=6
[sub].e ->3!=6
[subj].c ->2!=2
[subje][c][t] ->1!=1

So, 720+720+720+720+120+120+120+120+120+6+6+2+1 = 3495

4*6!+5*5!+2*3!+1*2!+0*1!+0*0!+1=3495

4*6! + 5*5! + 2*3! + 3 = 3495

B C E J S T U
before S --> B J C E
4 * 6! = 4 * 720 = 2880
S B ,S C, S E..S T = 5*5! = 5 * 120 = 600
S U B C, S U B E = 2*3! = 12
S U B J C = 2! = 2
S U B J E C T =1
rank = 2880 + 600 + 12 + 2 + 1 = 3495

4*6!=2880;
5*5!=600;
2*3!=12;
1*2!=2;
1*1!=1;
so 2880+600+12+2+1=3495.

first arrange d letters in alphabetical order.
for s=4*6!=2880
u=5*5!=600
b=0*4!=0
j=2*3!=12
e=1*2!=2 +1=3595

WORDS STARTING WITH B - - - - - -,
C - - - - - -,
E - - - - - -,
J - - - - - -,
AS WELL
S B - - - - -,
S C - - - - -,
S E - - - - -,
S J - - - - -,
S T - - - - -,
S U B C - - -,
S U B E - - -,
S U B J C - -,
WILL PRECEDE THE WORD SUBJECT
SO

WORDS STARTING WITH
B - - - - - - 6! WORDS I.E. 720
C - - - - - - 6! WORDS I.E. 720
E - - - - - - 6! WORDS I.E. 720
J - - - - - - 6! WORDS I.E. 720
S B - - - - - 5! WORDS I.E. 120
S C - - - - - 5! WORDS I.E. 120
S E - - - - - 5! WORDS I.E. 120
S J - - - - - 5! WORDS I.E. 120
S T - - - - - 5! WORDS I.E. 120
S U B C - - - 3! WORDS I.E. 6
S U B E - - - 3! WORDS I.E. 6
S U B J C - - 2! WORDS I.E. 2

ALL OF THEM WILL PRECEDE THE WORD SUBJECT,
HENCE
SUBJECT IS THE NEXT WORD IN THE ORDER SO THE RANK OF THE WORD IS 720+720+720+720+120+120+120+120+120+6+6+2+1 = 3495

WISH YOU GOOD LUCK

2880+600+12+2+1=3495