If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is

Step-by-step solution

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 ! × 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 .