Question

The letters of the word "LABOUR" are permuted in all possible ways, and the words thus formed are arranged as in a dictionary, then the rank of the word "LABOUR" is

• A. $240$
• B. $241$
• C. $242$
• D. $243$

Answer 1

The correct option is C $242$

Words starting with A $\to$

A

5

4

3

2

1

$C_1=5!$
Words starting with B $\to$

B

$C_2=5!$
$\to$ Next letter in the dictionary will be L.
The letters following it in the dictionary are A, B and O in order.
$\to$ So, the first word starting with L will be LABORU
$\to$ The one following it will be LABOUR
So, the rank of the word LABOUR is
$C_1+C_2+1+1$
$=5!+5!+1+1$
$=120+120+1+1$
$=242$
Ans $=242$