Question

If all the letters of the word $CHASM$ are rearranged to form $5$ letter word and are arranged in ascending order as in a dictionary, then the rank of the word $CHASM$ is

Answer 1

Given word is $CHASM$
Letters are $\{A,C,H,M,S\}$
Number of word starting with $A$ is $4!=24$
Then, the next word starts with
$CA\_\_\_.$
The remaining $3$ letters can be rearranged in $3!=6$ ways.
The next word is
$CHAMS$
Then
$CHASM$
Therefore, the rank of $CHASM$ is $24+6+2=32$