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JEE Main 2023 · Mathematics · Permutations and Combinations · medium

The number of arrangements of the letters of the word LETTER in which the two T's are not adjacent is

Single correct option

The number of arrangements of the letters of the word LETTER in which the two T's are not adjacent is
  1. A. 6060
  2. B. 120120
  3. C. 180180
  4. D. 240240
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Answer: (B) 120120

Total arrangements: 6!2! 2!=180\dfrac{6!}{2!\,2!}=180 (two T's and two E's repeated). Arrangements with both T's together: treat TT as one block, giving 5!2!=60\dfrac{5!}{2!}=60. Required number =180−60=120=180-60=120.
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Original question written in the JEE Main 2023 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake