Rank of the word RANKING in the dictionary of words formed by the letters of the word RANKING

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04 May 2017 Rank of the word

Rank of the word RANKING in the dictionary of words formed by the letters of the word RANKING

OPtion

1) 2208
2) 2209
3) 2210
4) 2212
5) 2214
6) 2211
7) 2206
8) 2204
9) 2202
10) None of these

Solution

Lets arrange the letters of RANKING alphabetically
AGIKNNR
Please note that only N is repeated twice

Words starting with letter A = 6!/2! = 360
Words starting with letter G = 6!/2! = 360
Words starting with letter I = 6!/2! = 360
Words starting with letter K = 6!/2! = 360
Words starting with letter N = 6! = 720

Words starting with letter RAG = 4!/2! = 12
Words starting with letter RAI = 4!/2! = 12
Words starting with letter RAK = 4!/2! = 12

Words starting with letter RANG = 3! = 6
Words starting with letter RANI = 3! = 6

Words starting with letter RANKG = 2! = 2

Words starting with letter RANKIG = 1 = 1

And next word is RANKING, so + 1 = 1

Sum of all = 4*360 + 720 + 3*12 + 2*6 + 2 + 1 +1 = 2212

Option 4)

Correct Option: 4 Best Solution (5)

Mukund Manohar   7 years AGO

Rank of the word RANKING
= (6/2!)*6! + (0/2!)*5! + (3/2!)*4! + (2/0!)*3! + (1/0!)*2! + (1/0!)*1! + (0/0!)*0! + 1
= 2160 + 0 + 36 + 12 + 2 + 1 + 0 + 1
= 2212

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Azim Uddin Siddiqui   7 years AGO

R A N K I N G( Assigning numerical values
6 1 5 4 3 5 2 according to the order of
alphabets)
6/2! *6! because there r six letters to the right of R(A,N,K,I,N,G)which are less than 6 rank and divided by 2! because N is repeating twice. multiply by 6! because starting from the right with 0! for G ,
1! for N,
2! for I
,...
and for R 6! .
Similarly no letters to the right of A which are less than 1, so 0/2!*5!= 0. Similarly solving,for each word, v get,
(6/2!*6!)+(0)+(3/2!*4!)+(2*3!)+(1*2!)+(1*1!)+(0)=2211
To this add 1 , v get 2211+1=2212 so option 4

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Himanshu Kesharwani   7 years AGO

2160+12+12+12+6+6+2+1 =2211 and then 2212th word is RANKING

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Ankit Kumar   7 years AGO

its 360+360+360+360+720+12+12+12+6+6+2+1=2211+1=2212

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Vahira Bollina   7 years AGO

Given word is RANKING
Alaphabetic order of give word is A,G,I,K,N,N,R
Number of words starts with A will be 6!/2!=360
G=6!/2!=360
I=6!/2!=360
k=6!/2!=360
N=6!/2!=360
N=6!/2!=360
RAG=4!/2!=12
RAI=4!/2!=12
RAK=4!/2!=12
RANG=3!=6
RANI=3!=6
RANKG=2!=2
RANKIG=1!=1
RANKING=0!=1
total=6(360)+3(12)+2(6)+2+1+1=2212

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