If the letters of the word MATHS are permuted and all possible...

The given word is MATHS

Arranging the letters alphabetically, we get

AHMST

When the word starts with any of the letters A/H/M/S, the number of possibilities$= 4 ! \times 4 = 96$

Now when the word starts with TA, then the number of possibilities$= 3 ! = 6$

Now when the word starts with THAMS, then the number of possibilities $= 1$

Rank $= 96 + 6 + 1 = 103$

Hence, rank of the work THAMS is $103$.