If letters of word CHASM are rearranged to form 5 letter words such that none of word repeat and results arranged in ascending order as in a dictionary what is rank of word CHASM?

The 5 letter word can be rearranged in 5! = 120 Ways without any of the letters repeating.
The first 24 of these words will start with A.
Then, the 25th word will start will CA _ _ _ .
The remaining 3 letters can be rearranged in 3! = 6 Ways.
i.e. 6 words exist that start with CA.
The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.
Therefore, the rank of CHASM will be 24 + 6 + 2 = 32