what will be the rank of word OPTION in the dictionary of words formed by letters of the word OPTION

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15 Aug 2013 rank

what will be the rank of word OPTION in the dictionary of words formed by letters of the word OPTION

OPtion

1) 176
2) 182
3) 185
4) 197
5) 201
6) 206
7) 212
8) 226
9) 248
10) none of these

Solution

OPTION
total no. of words formed = 6*5*4*3*2*1/2*1 = 360
arranged order I,N,O,O,P,T

RANK: (360/6)*2+(60*2/5)*3+(24/4)*3+(6/3)*0+(2/2)*1+1 = 212

Correct Option: 7 Best Solution (7)

siddhartha   10 years AGO

there are 5 letters in total I N O P T where O is can be used twice..

so in dictionary words start in alphabetical order

words starting with I are 5!/2=60
words starting with N are 5!/2=60
then words with O starts
words starting with OI are 4!=24
words starting with ON are 4!=24
words starting with OO are 4!=24
words staring with OPI OPN OPO are 3!+3!+3!=18
next are OPTINO and OPTION which are 2

so rank = 60 + 60 + 24 + 24 + 24 + 18 + 2
= 212

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ritesh kumar pandey   10 years AGO

before option the words will be from i and n and all words starting from oi, on, oo and all words from op
when all are calculated and added the sum will be 212.

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~Sandeep~   10 years AGO

Arranging alphabetically INOOPT
Counting words starting with various letter which comes before OPTION in dictionar ranking
[I/N](OOPT) -2*5*4*3 = 120
O[I/N](OPT) - 2*4*3*2 = 48
OO(INPT) - 4*3*2 = 24
OP-[I/N/O](T) - 3*3*2 = 18
OPTINO = 1
OPTION =1

Sum= 212

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mohini gupta   10 years AGO

first of all,I will be the first alphabet.after that arrangement of other five letters is 5! since O is twice hence it will be 5!/2=60.
again N will be the first letter similarly arrangement of other letters is 5!/2=60.
now O will be the first letter. then at second position firstly I will be placed and arrangement of other 4 is 4!.then N will be at second position.hence again 4!.then O will be at third hence again 4!. then T will be at third.now arrangement of other three is 3!.it will also happen thrice.then for last two O will come first then N will come.
hence, 5!/2+5!/2+4!+4!+4!+3!+3!+3!+1+1=212

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Chandni Maurya   10 years AGO

ans=(7) 212
arranging in alphabetic order (I,N,O,O,P,T)
starting with I = 5!/2
starting with N = 5!/2
starting with OI = 4!
starting with ON = 4!
starting with OO = 4!
starting with OPI = 3!
starting with OPN = 3!
starting with OPO = 3!
starting with OPTI= (N,O & O,N)=2
adding all of them =212

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Bingumalla Abinay   10 years AGO

OPTION

words that start with O= 2*5!/2!=120
2! to remove repetition's

120+72+18+1+1=212

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LOGAN WOLVERINE   10 years AGO

OPTION .
arrange the letters in alphabet order=INOOPT
I is the first letter we want. no.
I=5!/2!=60
N=5!/21=60
O is the letter we need. fix O.
again repeat the process.
[O]I=4!=24
[O]N=4!=24
[O]O=4!=24
[O]P is the letter we need. so fix [OP]
again repeat the process
[OP]I=3!=6
[OP]N=3!=6
[OP]O=3!=6
[OP]T is the letter we need . fix [OPT]
again proceed the same process
[OPT]I is the letter we need . fix [OPTI]
again do same process
[OPTI]N=1!=1
[OPTI]O is the letter we need. fix [OPTIO]
[OPTIO]N is the letter we need.
SO [OPTION]=1
sum all the values=60+60+24+24+24+6+6+6+1+1=212

so the answer is choice 7. 212

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