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Question: Answered & Verified by Expert
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
MathematicsPermutation CombinationJEE MainJEE Main 2023 (11 Apr Shift 2)
Options:
  • A

    103

  • B 102
  • C 101
  • D 104
Solution:
2375 Upvotes Verified Answer
The correct answer is:

103

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.

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