Rank of the word "NOTICE" in the dictionary of words formed by all the six letters of the word NOTIC

There are 6 letters and all are different : C E I N O T
In dictionary, words starting from C,E & I will come before word NOTICE.
so, total no. of words starting from C = 5!= 120
(we have to arrange 5 letters on five places)
similarly, no. of words starting from E = 5! = 120
and no. of words starting from I = 5! = 120
now, first word starting with letter N will come

similarly, no. of words starting with NC.... = 4!
no. of words starting with NE.... = 4!
no. of words starting with NI.... = 4!
now, words starting from NO will come

no. of words starting with NOC... =3!
no. of words starting with NOE... =3!
no. of words starting with NOI... =3!
now, words starting from NOT will come

no. of words starting with NOTC.. = 2!
no. of words starting with NOTE.. = 2!

then after words starting from NOTI will come and first word will NOTICE

so, total no. of words before NOTICE = 3*5! + 3* 4! + 3 * 3! + 2*2!
= 360 + 72 + 18 + 4
= 454
so, rank of NOTICE in dictionary = 455

1st we arrange the words of NOTICE in alphabet order
like,
C,E,I,N,O,T
Now strike off the first letter N.
Then count the no.of letters before N, and it is equal to 3,which is the coefficient of 5!.

Again strike off the letter O.
Then count the no.of letters before O and it is equal to 3 which is coefficient of 4!

Again strike off the first letter T.
Then count the no.of letters before T and it is equal to 3 which is coeffcient of 3!

Again strike off the first letter I.
Then count the no.of letters before I and it is equal to 2 which is coeffcient of 2!

Again strike off the first letter C.
Then count the no.of letters before C and it is equal to 0 which is coeffcient of 1!

Finally add 1 to the above values to get the rank of the word NOTICE as follows:

3*(5!) + 3*(4!) +3*(3!)+2(2!)+0(1!)+1 = 455
so option 6
that's it.

3*(5!)+ 3*(4!) + 3*(3!) + 2*(2!) +1 = 360+72+18+4+1 = 455

First arrange the given word in alphabetical order
CEINOT
1.search for N.Remove that word from list and see how many letters before N.. 3*(5!)=360
2.search for o.Remove that word from list and count the no of letters before o..3*(4!)=72
3.similarly , 3*(3!)=18
4. 2*(2!)=4
5. 0*(1!)=0
6. 1*(1!)=1
so sum=360+72+18+4+0+1=455
option 6)

Arranging the letters in alphabetical order we have, C,E,I,N,O,T

C_ _ _ _ _= 5!
E_ _ _ _ _= 5!
I_ _ _ _ _= 5!

NC_ _ _ _= 4!
NE_ _ _ _= 4!
NI_ _ _ _= 4!

NOC_ _ _= 3!
NOE_ _ _= 3!
NOI_ _ _= 3!

NOTC_ _= 2!
NOTE_ _= 2!

so, number of words before "NOTICE"= (3*5!)+(3*4!)+(3*3!)+(2*2!) = 454

SO, "NOTICE" will be 455th word.

option 6 is correct

The Letter starting with C,E,I,
5!+5!+5!
The letter statinr with
NC,NE,NI=4!+4!+4!
NOC,NOE,NOI=3!+3!+3!
The Letter Starting with:
NOTC,NOTE,=2!+2!
NOTICE=1
SO TOTAL:
5!+5!+5!+4!+4!+4!+3!+3!+3!+2!+2!+1

3*5!+3*4!+3*3!+2*2!+1*1!
=360+72+18+4+1=455

Arrange Notice in alphabetically order
NOTICE-> C,E,I,N,O,T
Now strike off the first letter N.

C,E,I,N,O,T

Then count the no.of letters before N, and it is equal to 3,which is the coefficient of 5!.

Again strike off the first letter O.
C,E,I,N,O,T

Then count the no.of letters before O and it is equal to 3 which is coefficient of 4!

Again strike off the first letter T.

C,E,I,N,O,T

Then count the no.of letters before T and it is equal to 3 which is coeffcient of 3!

Again strike off the first letter I.

C,E,I,N,O,T

Then count the no.of letters before I and it is equal to 2 which is coeffcient of 2!

Again strike off the first letter C.

C,E,I,N,O,T

Then count the no.of letters before C and it is equal to 0 which is coeffcient of 1!

Finally add 1 to the above values to get the rank of the word NOTICE as follows:

3(5!) + 3(4!) +3(3!)+2(2!)+0(1!)+1=455

rank= 3*5! +3*4! +3*3! +2*2! +0*1!+0*0! +1
= 455

The word is NOTICE .
We will arrange it alphabetically , then it be : CEINOT

Now , 3*5!+3*4!+3*3!+2*2!+0*1!+1 = 455

option is 6

Write the word in alphabetical order i.e. CEINOT
To write word NOTICE,
For 1st place Of N there are 3 letters C,E &I.
So it will be 3*5!
For next place i.e. NO there are 3 letters before O excluding N, because it is used on 1st place. So 3*4!
Similarly for others and expression would be
3*5!+3*4!+3*3!+2*2!+1=455

total number of words sarting from:
C = 5!
E = 5!
I = 5!
NC = 4!
NE = 4!
NI = 4!
NOC = 3!
NOE = 3!
NOI = 3!
NOTC = 2!
NOTE = 2!
then comes the word NOTICE.
So, rank of the word NOTICE is:
3 *5! + 3*4! +3*3!+5 =455

3*5! + 3*4! + 3*3! + 2*2! + 0*1! + 0*0! =360+72+18+4+0+0= 454+1= 455 is the answer.

In alphaetical order C,E,I,N,O,T
starting with letter C - 5!=120 words
starting with letter E - 5!=120 words
starting with letter I - 5!=120 words

starting with letter N- 5!=120
but IN "NOTICE"
start with NC-4!=24,NE-4!=24,NI-4!=24
NOC-3!=6,NOE-3!=6,NOI-3!=6,
for NOTICE-5
total rank=120+120+120+24+24+24+6+6+6+5=455

3*5! + 3*4! + 3*3! + 2*2! + 1(itself)
= 355

c_ _ _ _ _ = 5!
E _ _ _ _ _ = 5!
I _ _ _ _ _ = 5!
NC_ __ _ _= 4!
NE_ _ __ _= 4!
NI_ _ _ _ = 4!
NOC __ _ _= 3!
NOE __ _ _= 3!
NOI_ _ _= 3!
NOTC _ _= 2!
NOTE _ __= 2!
NOTICE= 0!
Totally 120+120+120+24+24+24+6+6+6+2+2+1 = 455

ans 455

5!+5!+5!+4!+4!+4!+3!+3!+3!+2!+2!+2

NOTICE:
arrange the letters in alphabetical order C,E,I,N,O,E
C_=5!=120
E_=5!=120
I_=5!=120
[N]C_=4!=24
[N]E_=4!=24
[N]I_=4!=24
[NO]C_=3!=6
[NO]E_=3!=6
[NO]I_=3!=6
[NOT]C_=2!=2
[NOT]E_=2!=2
[NOTICE]=1

sum the all values=120+120+120+24+24+24+6+6+6+2+2+1=455

for N 5!*3
for O 4!*3
for T 3!*3
for I 2!*2
+1 for CE

guessed

First C,E,I come before N so 3*5!=360
Then NC,NE,NI will come followed by other letters so 3*4!=72
Then NOC,NOE,NOI will come so 3*3!=18
Then NOTC,NOTE will come so 2*2!=4
Then NOTICE will be the next letter therefore
(360+72+18+4)+1=455th letter

C E I N O T in alphabetical order( NOTICE)

Now

C - No match = 5! =120

E- No match = 5! =120

I- no match = 5!=120

N- match so we move on to the next position

N C- no match = 4! =24

N E- no match= 4! = 24

N I-no match= 4! = 24

N O- match so we move on to the next position

N O C-no match= 3!= 6

N O E- no match = 3! = 6

N O I - no match = 3!= 6

N O T- match , so next position

N O T C - no match = 2 != 2

N O T E - no match = 2!= 2

N O T I- match next pos

N O T I C - match next

N O T I C E -full match so=1!= 1


now adding all= 120+120+120+24+24+24+6+6+6+2+2+1=455

so option 6)455 ans

C = 5!==120
E = 5!==120
i = 5!==120
NC = 4!==24
NE = 4!==24
NI = 4!==24
NOC = 3!=6
NOE = 3!==6
NOI = 3!==6
NOTC=2!==2
NOTE==2
NOTICE==1
add all= 120+120+120+24+24+24+6+6+6+2+2+1=455

CETNOT(DICTIONARY ORDER)
if C is fixed remaining can be arranged in 5! (120) ways
if E is fixed remaining can be arranged in 5! (120) ways
if I is fixed remaining can be arranged in 5! (120) ways
totally 360 ways
first letter N fixed
if C is fixed remaining can be arranged in 4! (24) ways
if E is fixed remaining can be arranged in 4! (24) ways
if I is fixed remaining can be arranged in 4! (24) ways
totally (360 +72) 432 ways
second letter NO fixed
like that.....
arranged in (6 +6 +6 = 18) ways
third letter NOT fixed
Remaining can arranged in 2! +2! = 4 ways
totally 454 ways
tourth letter NOTI fixed
454th word is NOTIEC
455th word is NOTICE
so answer is 455

455

fix I,C,E in 1st position and the remaining alphabets can be arranged in 5! ways so the total is 3×5!. then fix N in 1st and I,C,E in 2nd position so the remaining alphabets can be arranged in 4! ways and the total is 3×4! then fix N in 1st and O in 2nd position and I,C,E in 3rd position so the remaining alphabets can be arranged in 3! ways and the total is 3×3!.then NOTCIE , NOTCEI, NOTECI, NOTEIC then NOTICE so whole total is 455

i guessed.

NOTICE=CEINOT
=3*5!+3*4!+3*3!+2*2!+0*1!+1
=455

rearrange the word alphabetically and find the corresponding coefficints by striking each letter
CEINOT
strike N .no of letters before N = 3(5!)
strike O.no of letters before O = 3(4!)
strike T.no of letters before T =3(3!)
strike I.no of letters before I =2(2!)
strike C.no of letters before C =0(1!)
then add 1 so total rank =455

455 is the answer.

3*fact(5)+3*fact(4)+3*fact(3)+4

Word starting with C has 5!=120 combinations
Word starting with E has 5!=120 combinations
Word starting with I has 5!=120 combinations
Word starting with NC has 4!=24 combinations
Word starting with NE has 4!=24 combinations
Word starting with NI has 4!=24 combinations
Word starting with NOC has 3!=6 combinations
Word starting with NOE has 3!=6 combinations
Word starting with NOI has 3!=6 combinations
Word starting with NOTC has 2!=2 combinations
Word starting with NOTE has 2!=2 combinations
And, the next word is NOTICE
So,rank of this word is=(120+120+120+24+24+24+6+6+6+2+2+1)=455
So, option 6)455 is the right answer

N O T I C E
4 5 6 3 1 2
5! 4! 3! 2! 1! 0!
3 3 3 2 0 0 ====(5!*3)+4!*3)+............(0!*0)+1=455 answer 6 th option

starting with
C =5! =120
E= 5!=120
I =5!=120
NC=4!=24
NE=4!=24
NI=4!=24
NOC=6
NOE=6
NOI=6
NOTC=2
NOTE=2
NOTICE=1


120+120+120+24+24+24+6+6+6+2+2+1=455

3*5!+(3*4!)+(3*3!)+(2*2!)+1

answr is 6

notice
rank=455
option 6.

there is a shortcut process to calculate that rank
N O T I C E (we have to see no less than that
3 3 3 2 0 0 particular no.)
5! 4! 3! 2! 1! 0!
=(3*5!+3*4!+3*3!+2*2!)+1
=455

c*****=120
E*****=120
I*****=120
NC****=24
NE****=24
NI****=24
NOC***=6
NOE***=6
NOI***=6
NOTC**=2
NOTE**=2
NOTICE=1
=455

455 is the rank.

Given word : NOTICE
Alphabetical order : C E I N O T
words starting with C:
C - - - - - =5!=120
words starting with E:
E - - - - - =5!=120
words starting with I:
I - - - - - =5!=120
NC - - - - =4!=24
NE - - - - =4!=24
NI - - - - =4!=24
NOC - - - =3!=6
NOE - - - =3!=6
NOI - - - =3!=6
NOTC - - =2!=2
NOTE - - =2!=2
NOTICE=1
120+120+120+24+24+24+6+6+6+2+2+1 =455

this is the answer

Alphabets in NOTICE are in order
C
E
I
N
O
T

words forming from starting by C,E and I are 5! so total 3*5!
Now keeping fixed N ,words foriming from C,E,I are total 3*4!
now keeping NO fixed
words forming from C,E,I are total 3*3!

now keeping NOT fixed
words forming from C,E are total 2*2!
now keeping NOTI fixed next letter comes C and next one is E
so we found our word NOTICE
so its position is
3*5!+3*4!+3*3!+2*2!+1=455

notice corresponding position in alphabate
456312
now we have to find from first and see how much no. are less then that of first posion no.(4) there are three no. less then 4 ie; 3,2,1
and like this we find all the no less then position
like 4 5 6 3 1 2 corespondin no. of less no. then posional no.
3 3 3 2 0 0 now we have to write from last position 0!,1!,2!,3!,4!,5! and then multiply them with 3, 3, 3 ,2 ,0 ,0 corresponding and then sum all
like 0!*0+1!*0+2!*2+3!*3+4!*3+5!*3=455

Answer is 454+1 = 455

the rank will be 455

rank of word"NOTICE"=3(5!)+3(4!)+3(3!)+2(2!)+0(1!)+1
ans=455

Ans is 455.

Words start with
C-->120=5!
E-->120
I--->120
NC-->24=4!
NE-->24
NI--->24
NOC-->6=3!
NOE-->6
NOI--->6
NOTC-->2=2!
NOTE-->2=2!
NOTICE is the going to occur after all of the above cases in the dictionary.
so, (120*3)+(24*3)+(6*3)+(2*2)=454
NOTICE is the 455th word.

NOTICE write in alfabetical order and get ceinot and
first we take N .in CEINOT we see that N is after 3 words than 3 is the factor of !5 and so on and in last we add 1

using stroke and rank formula
C,E,I,N,O,T
rank=3*5!+3*4!+3*3!+2*2!+0*1!+0*1!+1
rank=455

Given word:
NOTICE

Arranging alphabetically
CEINOT

consider
first letter N
No of words before N in alpahbet order 3*5!(coefficient)

second letter O
No of words before O in alphabet order 3*4!
Remove N before counting

Likewise look for each alphabet
so finally 3(5!) + 3(4!) + 3(3!) + 2(2!) + 0(1!) +1 = 455

3*5!+3*4!+3*3!+2*2!+0*1+=455

NOTICE

Words starts from each letter = 6*5*4*3*2*1 =120
Before N, 3 letters I,C and E are there so after 3*120 = 360 words, words from N starts.

again after 1*3*4*3*2*1 = 72 words, words from NO starts...

again after 1*1*3*3*2*1 = 18 words, words from NOT starts...

again after 1*1*1*2*2*1 = 4 words, words from NOTI starts... which is NOTICE

so rank = 360+72+18+4+1 = 455

option is 6

Given word is NOTICE

The letters of the are N,O,T,I,C,E.

Write the alphabetical order of the letters of the given word 'NOTICE ' as C,E,I,N,O,T

Now strike off the first letter N.

C,E,I,N,O,T.

Then count the no.of letters before N, and it is equal to 3,which is the coefficient of 5!.

Again strike off the first letter O.

C,E,I,N,O,T

Then count the no.of letters before O and it is equal to 3 which is coefficient of 4!

Again strike off the first letter T.

C,E,I,N,O,T

Then count the no.of letters before T and it is equal to 3 which is coeffcient of 3!

Again strike off the first letter I.

C,E,I,N,O,T

Then count the no.of letters before I and it is equal to 2 which is coeffcient of 2!

Again strike off the first letter C.

C,E,I,N,O,T

Then count the no.of letters before C and it is equal to 0 which is coeffcient of 1!

Finally add 1 to the above values to get the rank of the word NOTICE as follows:

3(5!) + 3(4!) +3(3!)+2(2!)+0(1!)+1=455

NOTICE in alphabetical order gives CEINOT
Thus...
letters before N is 3,hence coefficient is 5
letters before O is 3,coefficient is 4
letters before T is 3,coefficient is 3
letters before I is 2,coefficient is 2
letters before C is 0,coefficient is 1
letters before E is 1,coefficient is 0

hence, 3(5!)+3(4!)+3(3!)+2(2!)+0(1!)+1=455

C,E,I comes before N, so word- 5!+5!+5!
NC,NE,NI words-- 4!+4!+4!
NOC,NOE,NOI-- 3!+3!+3!
NOTC,NOTE-- 2!+2!
total word=454.
so the rank is 455

position= 456312
NOTICE
(no of letters) 333200
less than)

3*5!+3*4!+3*3!+2*2!+1
360+72+18+4+1
=455

if we use permutation and combination we can find

Arranging the letters of "NOTICE" alphabetically, it will be C E I N O T
Keeping C as constant find the different combinations of words that can be formed using remaining 5 letters
5! = 120
Let me take each letter alphabetically
Keeping C as constant -> 120 words (5!)
Keeping E as constant -> 120 words (5!)
Keeping I as constant -> 120 words (5!)

Now, I can't take N as constant as NOTICE can appear anywhere between 120 combinations.
Take N and arrange remaining letters alphabetically (C E I O T). Now, take one by one along with N
Keeping N&C as constant -> 24 words (using E I O T... 4!)
Keeping N&E as constant -> 24 words (using C I O T... 4!)
Keeping N&I as constant -> 24 words (using C E O T... 4!)

Now, I can't take N&O as constant as NOTICE can appear anywhere between 24 combinations
Take N&O and arrange remaining letters alphabetically (C E I T). Now, take one by one along with N&O
Keeping N,O,C as constant -> 6 words (using E I T... 3!)
Keeping N,O,E as constant -> 6 words (using C I T... 3!)
Keeping N,O,I as constant -> 6 words (using C E T... 3!)

Now, I can't take N,O,T as constant as NOTICE can appear anywhere between 6 combinations.
Take N,O,T and arrange the remaining letters alphabetically(C E I). Now, take one by one
Keeping N,O,T,C as constant -> 2 words (using E I... 2!)
Keeping N,O,T,E as constant -> 2 words (using C I... 2!)
Now, if you take N,O,T,I as constant the first possible word (alphabetically) is NOTICE

Now, add all the above combinations
(120+120+120) + (24+24+24) + (6+6+6) + 2+2+1
=> 360+72+18+5
=> 455

Rank of the word NOTICE will be 455

Option 6.