JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Permutations and Combinations

The letters of MATHS in alphabetical order are A, H, M, S, T. Words beginning with each of A, H, M and S use the remaining four letters in $4!=24$ ways, contributing $4\times 24=96$ words before any word starting with T. Among the words starting with T, those with second letter A number $3!=6$, after which words with second letter H begin. The first TH-word in dictionary order is THAMS itself, because its remaining letters A, M, S are already in ascending order. Therefore the serial number of THAMS is $96+6+1=103$.