Find Rank of the word SWATANTRA in the dictionary of words formed by the letters of the word SWATANT

M4maths Previous Puzzles

15 Aug 2017 Happy Independence Day!

Find Rank of the word SWATANTRA in the dictionary of words formed by the letters of the word SWATANTRA

OPtion

1) 19472
2) 19772
3) 19172
4) 19272
5) 19372
6) 19572
7) 19672
8) 19872
9) 19972
10) None of these

Solution

Lets arrange the letters alphabetically = AAANRSTTW

Words starting with A = 8!/(2!*2!) = 10080
Words starting with N = 8!/(3!*2!) = 3360
Words starting with R = 8!/(3!*2!) = 3360
Words starting with SA = 7!/(2!*2!) = 1260
Words starting with SN = 7!/(3!*2!) = 420
Words starting with SR = 7!/(3!*2!) = 420
Words starting with ST = 7!/(3!) = 840
Words starting with SWAA = 5!/(2!) = 60
Words starting with SWAN = 5!/(2!*2!) = 30
Words starting with SWAR = 5!/(2!*2!) = 30
Words starting with SWATAA = 3! = 6
Words starting with SWATANA = 2! = 2
Words starting with SWATANR = 2! = 2
Words starting with SWATANTA = 1 = 1
And next word is SWATANTRA so + 1

Sum of all = 19872
Option 8)

Correct Option: 8 Best Solution (6)

G.S.Kantharao   7 years AGO

Word is SWATANTRA
Order is AAANRSTTW
Words with A=8!/2!*2!=10080
With N = 8!/3!*2! =3360
With R =8!/3!*2!=3360
With SA =7!/2!*2!=1260
With SN = 7!/3!*2!= 420
WithSR 7!/3!*2!=420
With ST=7!/3!=840
With SWAA=5!/2!=60
With SWAN=5!/2!*2!=30
With SWAR = 5!/2!*2!=30
With SWATA=3!=6
With SWATANA =2!=2
With SWATANR = 2!=2
With SWATANTA =1
With SWATANTRA=1
Total rank =10080+3360+3360+1260+420+420+840+60+30+30+6+2+2+1+1=19872
Hence the right option is 8👈

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Varun   7 years AGO

5*8!/(3!2!) + 7*7!/(3!2!)+0*6!/(3!*2!)+4*4!/(2!*2!)+...+1*1!/(1)+0*0!/(0) + 1 = 19872

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kasarla swathi   7 years AGO

provide alphabetical order numbering:
s w a t a n t r a
4 6 15 1 2 5 3 1
now find the number of digits less than 4,6,... in forward direction like
5 7 0 4 0 1 2 1 0
now divide each one with the number of repetatives including them we get
5/3!2! 7/3!2! 0/3!2! 4/2!2! 0/2! 1/1! 2/1! 1/1! 0/1!
now multiply each term with their factorials starting from 0! right we get
16800 2940 120 6 4 1
now add them we get 19871

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pooja   7 years AGO

S W A T A N T R A
4 6 1 5 1 2 5 3 1
alphabetical arrangement
((5/(3!2!))*8!)+((7/(3!2!))*7!)+(0*6!)+((4/(2!2!))*5!)+(0*4!)+((1/0!)*3!)+((2/0!)*2!)+((1/0!)*1!)+((0/0!)*0!)=19871
19871+1=19872

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himadhar   7 years AGO

A-10080
N-3360
R-3360
SA-1260
SN-420
SR-420
ST-840
SWN-30
SWAN-30
SWAR-2
SWATANTRA-1

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Mukund Manohar   7 years AGO

Rank of the word SWATANTRA
= 5/(3!*2!) + 7/(3!*2!) + 0/(3!*2!) + 4/(2!*2!) + 0/2! + 1/0! + 2/0! + 1/0! + 0/0!
= 16800+2940+0+120+0+6+4+1+0+1 = 19871 + 1 = 19872

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