Number of words starting with a=(8!/2!*2!)=10080
Number of words starting with d=(8!/2!)=20160
Number of words starting with e=(8!/2!)=20160
Number of words starting with n=(8!/2!*2!)=10080
Number of words starting with s=(8!/2!*2!)=10080
Number of words starting with wa=(7!/2!*2!)=1260
Number of words starting with wd=(7!/2!)=2520
Number of words starting with wea=(6!/2!)=360
Number of words starting with weda=5!=120
Number of words starting with wedd=5!=120
Number of words starting with wede=5!=120
Number of words starting with wedna=4!=24
Number of words starting with wednd=4!=24
Number of words starting with wednea=3!=6
Number of words starting with wedned=3!=6
Number of words starting with wednesa=2!=2
Number of words starting with wednesda=1!=1
So rank=10080+20160+20160+10080+10080+1260+2520+360+120+120+120+24+24+6+6+2+1=75123
So option 9)75123 is the right answer

The alphabets in the word "WEDNESDAY" in numbers are A=1,D=2,E=2,N=1,S=1,W=1,Y=1 . There are 7 alphabets in which 2 are repeated 2 times.
To get the rank of "WEDNESDAY" we need to check the number of words that can be formed before "WEDNESDAY".
From A 8!/(2!2!) words can be formed.
From D 8!/2! words can be formed.
From E 8!/2! words can be formed.
From N 8!/(2!2!) words can be formed.
From S 8!/(2!2!) words can be formed.
Now starting with W number of words that can be formed before "WEDNESDAY" are
WA = 7!/(2!2!)
WD = 7!/2!
WEA = 6!/2!
WEDA = 5!
WEDD = 5!
WEDE = 5!
WEDNA = 4!
WEDND = 4!
WEDNEA = 3!
WEDNED = 3!
WEDNEN = 3!
WEDNESA = 2!
WEDNESDAY

guessed

6 3 2 4 3 5 2 1 7
W E D N E S D A Y
(7/(2!*2!))(8!)+(3/(2!*2!))(7!)+(1/2!)(6!)+(3/1!)(5!)+(2/1!)(4!)+(2/1!)(3!)+(1/1!)(2!)+(0/1!)(1!)+(0/1!)(0!)+1
70560+3780+360+360+48+12+2+1
Ans:75123

its 75123...

6 3 2 4 3 5 2 1 7
W E D N E S D A Y
7/2!*2! 3/2!*2! 1/2! 3/1! 2/1! 2/1! 1/1! 0/1! 0/1!

8! 7! 6! 5! 4! 3! 2! 1! 0!

Now rank of WEDNESDAY= (7/2!*2!) *8! + (3/2!*2!) *7! + (1/2!)*6! + (3/1!)*5! + (2/1!)*4! + (2/1!)*3! + (1/1!)*2! + (0/1!)*1! + ( 0/1!)0! + "1" =75123

i.e. Option 9)

6 3 2 4 3 5 2 1 7
W E D N E S D A Y
7/2!*2! 3/2!*2! 1/2! 3/1! 2/1! 2/1! 1/1! 0/1! 0/1!

8! 7! 6! 5! 4! 3! 2! 1! 0!

Now rank of WEDNESDAY= (7/2!*2!) *8! + (3/2!*2!) *7! + (1/2!)*6! + (3/1!)*5! + (2/1!)*4! + (2/1!)*3! + (1/1!)*2! + (0/1!)*1! + ( 0/1!)0! + "1" =75123

i.e. Option 9)

answer is 75,123

arrange the letters ascending order in the given word: ADDEENSWY,thencalculating of the rank words stating with A=8!/2!2!=10080,like wise after calculation wednesday is 75123

8!/4 + 8!/2 + 8!/2 + 7!/4 + 7!/2 + 6!/2 + 5! + 5! + 5! + 4! + 4! + 3! +3! + 2! + 1
=75123

the rank will be 9

Letters are : A D D E E N S W Y
words starting with A= 8!/2!2!= 10080
Similarly words starting with D= 20160
With E= 20160
With N= 10080
With S= 10080
The total is 70560
Now the words with WA= 7!/2!2!= 1260
With WD= 2520
similarly by applying permutations, the total number of words before Wednesday are 75122
Hence rank of WEDNESDAY is 75123

since words are repeated we use the following calculation:
rank of wednesday=(7*8!/(2!*2!))+(3*7!/(2!*2!))+(1*6!/2!)+(3*5!/1!)+(2*4!/1!)+(2*3!/1!)+(1*2!/1!)+(0*1!/1!)+(0*0!/1!)+1

rank of wefnesday=70560+3780+360+360+48+12+2+0+0+1

ranks of wednesday=75123

option 9

Option)9