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Solution


Q.

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             [2023]
1 103   
2 104   
3 101  
4 102  

Ans.

(1)

Given word is MATHS.

In alphabetical order: A, H, M, S, T

Now, word starting with

A_ _ _ _ i.e., 4! ; H_ _ _ _  i.e., 4!

M_ _ _ _ i.e., 4! ; S_ _ _ _  i.e., 4!

T A_ _ _  i.e., 3! ; T H A M S i.e., 1

∴   Rank of the word THAMS=4×4!+1×3!+1=103