Mathematics - Permutation & Combination Question with Solution | TestHub

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 $103$.