Rank of the word TUESDAY in the dictionary of words formed by the letters of the word TUESDAY.

alphabetical order of TUESDAY is
A,D,E,S,T,U,Y
case1:
total word that start with letter 'A'=6*5*4*3*2*1=720
total word that start with letter 'D'=6*5*4*3*2*1=720
total word that start with letter 'E'=6*5*4*3*2*1=720
total word that start with letter 'S'=6*5*4*3*2*1=720
case2:
total word that start with 'TA'=5*4*3*2*1=120
total word that start with 'TD'=5*4*3*2*1=120
total word that start with 'TE'=5*4*3*2*1=120
total word that start with 'TS'=5*4*3*2*1=120

case3:
total word that start with 'TUA'=4*3*2*1=24
total word that start with 'TUD'=4*3*2*1=24

case4:
total words that start with 'TUEA'=3*2*1=6
total words that start with 'TUED'=3*2*1=6

case5:
total words that start with 'TUESA'=2*1=2

case 6:
And word start with 'TUESD'=2 ie 'TUESDAY' and 'TUESDYA'

so rank of TUESDAY is =(4*720)+(4*120)+(2*24)+(2*6)+2+1=3423

(6!*4)+(5!*4)+(4!*2)+(3!*2)+(2!*1)+1 = 3423

ADESTUY

Rank of TUESDAY =
4*6! + 4*5! + 2*4! + 2*3! + 2! + 1
= 3423

T(4*6!)+U(4*5!)+E(2*4!)+S(2*3!)+D(1*2!)=3422
So rank of TUESDAY is 3423.

The possible words that can be formed and
and also alphabetically
A*6!+D*6!+E*6!+S*6!
TA*5!+TD*5!+TE*5!+TE*5!
TUA*4!+TUD*4!
TUEA*3!+TUED*3!
TUESA*2!
TUESDA*1!
The rank =(6!*4)+(5!*4)+(4!*2)+(3!*2)+2!+1!=3423