Question

If all the letters of the word $RANK$ are rearranged to form $4$ letter words and arranged in ascending order as in a dictionary, then the rank of the word $RANK$ is

• A. $22$
• B. $19$
• C. $20$
• D. $21$

Answer 1

The correct option is C $20$

Given letters are $\{A,K,N,R\}$
Word starting with $A$ in the dicitionary $=3!=6$
Word starting with $K$ in the dicitionary $=3!=6$
Word starting with $N$ in the dicitionary $=3!=6$
Then
$RAKNRANK$
$\therefore$ The rank $={20}^{th}$