Easy Permutation-Combination Solved QuestionAptitude Discussion

 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

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
()

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.....

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