M4maths Previous Puzzles

07 Jul 2017 Rank of the word

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

OPtion

1) 127921
2) 121952
3) 127949
4) 127952
5) 127951
6) 127948
7) 127852
8) 27183
9) 123952
10) None of these

Solution

THURSDAYS
Lets arrange the letters alphabetically = ADHRSSTUY

Words starting with A = 8!/(2!) = 20,160
Words starting with D = 8!/(2!) = 20,160
Words starting with H = 8!/(2!) = 20,160
Words starting with R = 8!/(2!) = 20,160
Words starting with S = 8! = 40320
Words starting with TA = 7!/(2!) = 2520
Words starting with TD = 7!/(2!) = 2520
Words starting with THA = 6!/(2!) = 360
Words starting with THD = 6!/(2!) = 360
Words starting with THR = 6!/(2!) = 360
Words starting with THS = 6! = 720

Words starting with THUA = 5!/(2!) = 60
Words starting with THUD = 5!/(2!) = 60

Words starting with THURA = 4!/(2!) = 12
Words starting with THURD = 4!/(2!) = 12

Words starting with THURSA = 3! = 6

Words starting with THURSDAS = 1

and next word is :
THURSDAYS = 1

Sum of all = 127952

Correct Option: 4 Best Solution (6)

Mukund Manohar   7 years AGO

Rank of the word THURSDAYS
= (6/2!)*8! + (2/2!)*7! + (5/2!)*6! + (2/2!)*5! + (2/2!)*4! + (1/0!)*3! + (0/0!)*2! + (1/0!)*1! + (0/0!)*0! + 1
= 120960 + 5040 + 1800 + 120 + 24 + 6 + 0 + 1 + 0 + 1
= 127952

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Sonu Kumar   7 years AGO

"THURSDAYS"

6 3 7 4 5 2 1 8 5
T H U R S D A Y S
T---6/2!*8!
H---2/2!*7!
U---5/2!*6!
R---2/2!*5!
S---2/2!*4!
D---1/0!*3!
A---0/0!*2!
Y---1/0!*1!
S---0/0!*0!

Find the multiplying value and sum them
Sum=120961+5040+1800+120+24+6+0+1+0
sum=127951+1
Rank of the "THURSDAYS"=sum+1=127952
a correct answer is 4)127952

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G.S.Kantharao   7 years AGO

Arranging alphabetically= A,D,H,R,S,S,T,U,Y(S repeated twice)
Words which started with A=8!/2!=20160
Words with D= 8!/2!=20160
Words with H=8!/2!=20160
Words with R= 8!/2!= 20160
Words with S= (8!/2!)*2=40320
Words. Which starts with TA=7!/2!=2520
With TD=2520
Words which starts with THA=6!/2!=360
With THD= 6!/2=360
With THR= 6!/2!=360
With THS = (6!/2!)*2=720
Words with THUA =5!/2!=60
Words with THUD = 5!/2!=60
Words with THURA= 4!/2!=12
With THURD=4!/2!=12
With THURSA = 3!=6
With THURSDAS=1
Word with THURSDAYS=1
Rank of the Word THURSDAYS=
20160+20160+20160+20160+40320+2520+2520+360+360+360+720+60+60+12+12+6+1+1=129952
Hence the right option is 4

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NABA KISHORE PADHY   7 years AGO

Answer is 127952. THURSDAYS has 9 letters and s repeated twice.

Words with A = 8!/2, words with D = 8!/2, words with H = 8!/2, Words words with R = 8!/2, with S = 8!, with TA = 7!/2, TD = 7!/2, THA = 6!/2, THD = 6!/2,THR = 6!/2, THS =6!,
THUA = 5!/2, THUD = 5!/2 THURA = 4!/2, THURD 4!/2,
THURSA = 3!, THURSDA (SY & YS) = 2. Add all and answer is 127952

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Vahira Bollina   7 years AGO

given word is THURSDAYS
Alphabetical order of given word is A,D,H,R,S,S,T,U,Y
First letter starts with A is 8!/2!=20,160
D is 8!/2!
H is 8!/2!
R is 8!/2!
S is 8!/2!
S is 8!/2!
TA is 7!/2!
TD is 7!/2!
THA is 6!/2!
THD is 6!/2!
THR is 6!/2!
THS is 6!/2!
THS is 6!/2!
THUA is 5!/2!
THUD is 5!/2!
THURA is 4!/2!
THURD is 4!/2!
THURSA is 3!
THURSDAS is 1!
THURSDAYS is 0!

6(8!/2!)+2(7!/2!)+5(6!/2!)+2(5!/2!)+2(4!/2!)+3!+1!+0!=127952

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T.J.Keerthana priya   7 years AGO

t h u r s d a y s
6 3 7 4 5 2 1 8 5
6/2! 2/2! 5/2! 2/2! 2/2! 1/1! 0 1 0
8! 7! 6! 5! 4! 3! 2! 1! 0!
multiply the previous 2 steps and add the results and then u get 127951.......then add 1 then it become 127952

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