Question

The letter's of the word $LABOUR$ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. The rank of the word $LABOUR$ will be

• A. $239$
• B. $240$
• C. $241$
• D. $242$

Answer 1

The correct option is D $242$

Alphabets present in the word $LABOUR$ are $(L,A,B,O,U,R)$
Order of these letters according to the dictionary is $A,B,L,O,R,U$
With $A$ in the beginning $\left(A\_\_\_\_\_\right)$, the remaining letters can be permuted in $5!$ ways.

Similarly, with $B$ in the beginning $\left(B\_\_\_\_\_\right)$, the remaining letters can be permuted in $5!$ ways.

With $L$ in the beginning $\left(L\_\_\_\_\_\right)$, the first word will be $LABORU,$
the second will be $LABOUR.$
Hence, the rank of the word $LABOUR$ is
$=5!+5!+2$
$=242$