Question

The letters of the word "RACE" are arranged in all possible ways and the words thus formed are arranged in a dictionary. The rank of the word "CARE" is

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (B)

$8$

When arranged in dictionary, words starting with $A$ start first
$\Rightarrow$ Total number of words staring with $A$ are $3!$ = $6$
Words starting with C are followed with A first, the other two letters can be arranged in two ways.
$\Rightarrow$ words are CAER and CARE.
$\therefore$ Rank of CARE is $8$.