Find Rank of the word SHIVRATRI in the dictionary of words formed by the letters of the word SHIVRAT

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23 Feb 2017 Rank of word

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

OPtion

1) 62219
2) 62220
3) 62229
4) 62230
5) 62239
6) 62240
7) 62249
8) 62250
9) 62259
10)None of these

Solution

SHIVRATRI => AHIIRRSTV
Arranging letters in alphabetical order: AHIIRRSTV => I and R are repeated (2 I’s& 2 R’s)
Words starting with Alphabet A = 8!/(2!*2!) = 10080
Words starting with Alphabet H = 8!/(2!*2!) = 10080
Words starting with Alphabet I = 8!/2! = 20160
Words starting with Alphabet R = 8!/2! = 20160
Words starting with Alphabet SA = 7!/(2!*2!) = 1260
Words starting with Alphabet SHA = 6!/(2!*2!) = 180
Words starting with Alphabet SHIA = 5!/2! = 60
Words starting with Alphabet SHII = 5!/2! = 60
Words starting with Alphabet SHIR = 5! = 120
Words starting with Alphabet SHIT = 5!/2! = 60
Words starting with Alphabet SHIVA = 4!/2! =12
Words starting with Alphabet SHIVI = 4!/2! = 12
Words starting with Alphabet SHIVRAI = 2! = 2
Words starting with Alphabet SHIVRAR = 2! = 2
Words starting with Alphabet SHIVRATI = 1 = 1
And next word is SHIVRATRI so +1 for final word
Sum of all words => 2*10080 + 2*20160 + 1260 + 180+ 3*60 + 120 + 2*12 + 2*2 + 1 + 1 =62250

Option 8)

Correct Option: 8 Best Solution (2)

DIVYANSHU SHEKHAR   7 years AGO

Taking the letter K instead
A - (8!/2!*2!)=10080,
H- (8!/2!*2!)=10080,
I - (8!/2!)=20160,
R - (8!/2!)=20160,
S A - (7!/2*2!)=1260,
S H A - (6!/2!*2!)=180,
S H I A - (5!/2!)=60,
S H I I - (5!/2!)=60,
S H I R - (5!)=120,
S H I T - (5!/2!)=60,
S H I K A - (4!/2!)=12,
S H I K I - (4!/2!)=12,
S H I K R A I - (2!)=2,
S H I K R A R - (2!)=2,
S H I K R A T I R (1!)=1,
S H I K R A T R I (1!)=1
Rank=(10080+10080+20160+20160+1260+180+60+60+120+60+12+12+2+2+1+1)=62250

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RANJEET KUMAR   7 years AGO

SHIVRATRI,
order = 5, 2, 3, 7, 4, 1, 6, 4, 3
now multiply with corresponding multiplier.
we will get 62249+1 = 62250

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