Permutation-Combination
Aptitude

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Q.

The letter of the word $LABOUR$ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word $LABOUR$?

 A.

275

 B.

251

 C.

240

 D.

242

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Solution:
Option(D) is correct

The order of each letter in the dictionary is $ABLORU$.

Now, with $A$ in the beginning, the remaining letters can be permuted in $5!$ ways.

Similarly, with $B$ in the beginning, the remaining letters can be permuted in $5!$ ways.

With $L$ in the beginning, the first word will be $LABORU$, the second will be $LABOUR$.

Hence, the rank of the word $LABOUR$ is $5!+5!+2$

$= 242$


(5) Comment(s)


Bet
 ()

what happened with the $U$??


Joe
 ()

What about it?

Since, $U$ comes at the last, it be ignored anyway.


Renu
 ()

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Leelanand
 ()

I am not getting this answer. could you please explain more elaborately......


MALLIKARJUN
 ()

mr.leelanand the meaning of the question is if u arrange the word as in dictionary order at what rank u will get the word labour....

so if u arrange with A as first letter the reamaining letter can be permuted as 5! anf if b as first letter again 5! and then if L as first letter there is only two possibiltiy first is laboru then labour.....

$so 5!+5!+2=242$