What will be the rank of the word "JAIMATADI" in the dictionary of the words formed by using letter

M4maths Previous Puzzles

06 Aug 2015 Rank of word

What will be the rank of the word "JAIMATADI" in the dictionary of the words formed by using letter of the word "JAIMATADI". (You have to use all letter in every word)

OPtion

1) 24671
2) 19675
3) 17444
4) 16351
5) 21972
6) 22473
7) 20959
8) 17868
9) 18920
10)21797

Solution

Total number of word formed = 9*8*7*6*5*4*3*2*1/ 3*2*1*2*1
(Denominator is due to repetition of A & I)
= 30240

Now rank of JAIMATADI in dictionary
20160+540+240+18+1 = 20959

Option 7)

Correct Option: 7 Best Solution (16)

Deven Patidar   9 years AGO

AAA D II J M T

A 10080
D 3360
I 6720
J A A 360
J A D 180
J A I A 120
J A I D 60
J A I I 60
J A I M A A 6
J A I M A D 6
J A I M A I 6
J A I M A T A D I 1 = 20959

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Megha Goel   9 years AGO

JAIMATADI contains A-3 D-1 I-2 J-1 M-1 T-1 i.e. 9 letters
words from A _ _ _ _ _ _ _ = 8!/(2!*2!)= 10080
D _ _ _ _ _ _ _ _ = 8!/(3!*2!)=3360
I _ _ _ _ _ _ _ _=8!/(3!)=6720
JAA _ _ _ _ _ _= 6!/2!
JAD _ _ _ _ _ _ =6!/(2!*2!)
JAIA _ _ _ _ _=5!
JAID _ _ _ _ _ =5!/2!
JAII _ _ _ _ _=5!/2!
JAIMAA _ _ _ =3!
JAIMAD _ _ _=3!
JAIMAI _ _ _=3!
next word will be JAIMATADI . Hence adding these numbers we get 20958 and RAnk of word JAIMATADI is 20959.

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sudhir kumar maurya   9 years AGO

arrange in order A,A,A,D,I,I,J,M,T
no. of letters starting with A=8!/2!2! (divide becoz A and I repeated twice)
no. of letters with D = 8!/3!2!(divide by 3! and 2! becoz A and I repeated 3 times and 2 times resp. )
no. of letters with I =8!/3!
next letter will be J so fix J
after J it is A so fix JA after this
no. of letters with A = 6!/2!
no. of letters with D = 6!/2!2!
next letter will be I
so fix JAI
no. of letters with A = 5!
no. of letters with D = 5!/2!
no. of letters with I = 5!/2!
fix JAIMA
no. of letters with A = 3!
no. of letters with D = 3!
no. of letters with I = 3!
fix JAIMATADI
add all factorial + 1 =20959

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Abhishek Sneh   9 years AGO

make JAIMATADI in rank wise ....
like =JAIMATADI
J=4,A=1,I=3,M=5,A=1,T=6,A=1,D=2,I=3

first take J and check the number who less than the valu of J like a,i,a,a,d,i =6 so in this there are a many time i many times so we have to write like 6/3!x2! x8! =20160
for I = 3/2!x2!x6!=540
for M=2!x5!=240
for T =3x3!=18
NOTE rest we leave because something multiply in "0" is equal to 0 ,
after adding all the number we get
20160+540+240+18=20958
add 1 for the position of JAIMATADI = 20959

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Debabrata Dey   9 years AGO

8!/2!2!+8!/3!2!+8!/3!+6!/2!+6!/2!2!+5!+5!/2!+5!/2!+3!+3!+3!+1
=20959

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Dinni   9 years AGO

Arranging in alphabetical order to determine rank of the word JAIMATADI
AAADIIJMT
A - 8!/4
D - 8!/12
I - 8!/6
(JA)A - 6!/2
(JA)D - 6!/4
(JAI)A- 5!
(JAI)D- 5!/2
(JAI)I - 5!/2
(JAIMA)A- 3!
(JAIMA)D- 3!
(JAIMA)I - 3!
(JAIMAT) ADI - 1
Adding we get 20959

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vinusha   9 years AGO

A - 8!/4
D - 8!/12
I - 8!/6
(JA)A - 6!/2
(JA)D - 6!/4
(JAI)A- 5!
(JAI)D- 5!/2
(JAI)I - 5!/2
(JAIMA)A- 3!
(JAIMA)D- 3!
(JAIMA)I - 3!
(JAIMAT) ADI - 1
10080+3360+6720+360+240+180+18+1
20959.

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Kundan Gope   9 years AGO

J A I M A T A D I
_____________________________________________________
4 1 3 5 1 6 1 2 3
_____________________________________________________
6 0 3 4 0 3 0 0 0
---- ----- -----
3!2! 2!2! 2!
_____________________________________________________
X X X X X X X X X
8! 7! 6! 5! 4! 3! 2! 1! 0!

=20160+0+540+240+0+18+0+0+0
=20958
The rank of word is= 20958+1= 20959 (Ans)

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Deepak kumar kumawat   9 years AGO

JAIMATADI there is 9 words
arranging words in alphabatic order
AAADIIJMT
WORD START FROM A= 8!/2!*2!=10080
D=8!/(3!*2!)= 3360
I= 8!/3!=6720
WORD START FROM JA
[JA]A=6!/2!= 360
[JA]D= 6!/(2!*2!)= 180
NOW WORD STARTS FROM JAI
[JAI]A=5!=120
[JAI]D=5!/2!=60
[JAI]I=5!/2!=60
WORD START FROM JAIMA
[JAIMA]A=3!=6
[JAIMA]D=3!
[JAIMA]I=3!
JAIMATADI=1
SO rank of jaimatadi is 10080+3360+6720+360+180+120+60+60+18+1=20959

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Narendra Gopi   9 years AGO

A...........8!/2!*2! =10080
D............8!/3!*2! =3360
I............8!/3! = 6720
J
JA
JAA.......6!/2! =360
JAD........6!/2!*2! =180
JAI
JAIA.......5! =120
JAID........5!/2! =60
JAII..........5!/2! =60
JAIM
JAIMA
JAIMAA.........3! =6
JAIMAD.......3!/2! =3
JAIMAI.........3!/2! =3
JAIMAT
JAIMATA
JAIMATAD
JAIMATADI
Total The word JAIMATADI=20959

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aman agrawal   9 years AGO

in word JAIMATADI first of all we give a temporary no to each alphabet according to the priority of alphabet.so "A" will get 1 priority similarly "D"will get 2 priority & so on.
now from the first letter we check how much priorities are smaller than this (so in case of "J" there are 6 letters whose priority is lesser than the j's priority)
(6/3!*2!)*8!+(3/2!*2!)*6!+(4/2!)*5!+(3/0!)*3!+1 will give the rank of the word"JAIMATADI" which is 20959.

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RAKESH   9 years AGO

8!(1/4 +1/12 + 1/6) + 6!(1/2 +1/4) + 5!(1+ 1/2 +1/2) + 3*3! + 1

= 20959

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SOMA NARESH   9 years AGO

give the numbers according to alphabetical order as
A=1, D=2, I=3, J=4, M=5, T=6
now
Order of Letters J=3 A=1 I=3 M=5 A=1 T=6 A=1 D=2 I=3
For J = 4*8!/(3!*2!) = 20160
For A = 0*7!/(3!*2!) = 0
For I = 3*6!/(2!*2!) = 540
For M = 4*5!/(2!) = 240
For A = 0*4!/2! = 0
For T = 3*3! = 18
For A = 0*2! = 0
For D = 0*1! = 0
For I = 0*0! = 0
For the word JAIMATADI = 1
Total sum = 20160 + 540 + 240+ 18 + 1 = 20959

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Soma Naresh   9 years AGO

give the numbers according to alphabetical order as
A=1, D=2, I=3, J=4, M=5, T=6
now
Order of Letters J=3 A=1 I=3 M=5 A=1 T=6 A=1 D=2 I=3
For J = 4*8!/(3!*2!) = 20160
For A = 0*7!/(3!*2!) = 0
For I = 3*6!/(2!*2!) = 540
For M = 4*5!/(2!) = 240
For A = 0*4!/2! = 0
For T = 3*3! = 18
For A = 0*2! = 0
For D = 0*1! = 0
For I = 0*0! = 0
For the word JAIMATADI = 1
Total sum = 20160 + 540 + 240+ 18 + 1 = 20959

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jomon v j   9 years AGO

A -10080
D -3360

I -6720
JAA-360
JAD- 180
JAIA-120
JAID-60
JAII-60
JAIMAA-6
JAIMAD -6
JAIMAI -6
JAIMATADI-1

TOTAL =20959

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Abhishek Anand   9 years AGO

Explanation :
Write Down the WORD JAIMATADI and assign each letter a value

4 1 3 5 1 6 1 2 3
J A I M A T A D I

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

now look for the smaller value than 4 towards its ryt side
6 no. are there which is lesser than 4
And,also look how many times letters are repeating .

And then write expression in this manner...

6 / 3!x2! 0/3!x2! 3/2!x2!.....so on upto 0/0!

now multiply the above expression corresponding to the factorials written below to that letter and add them !
At last +1 to the resulting sum !
u got the Answer as 20959! Thanks !

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