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NDA 2025 Maths · Mathematics · Permutations and Combinations · hard

The number of arrangements of the letters of the word LEVEL in which the two E's are not together is

Single correct option

The number of arrangements of the letters of the word LEVEL in which the two E's are not together is
  1. A. 1212
  2. B. 2424
  3. C. 1818
  4. D. 3030
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Answer: (C) 1818

Total arrangements: 5!2! 2!=30\frac{5!}{2!\,2!}=30 (L and E both repeat). Treating EE as one block gives 4!/2!=124!/2!=12 arrangements with E's together. Required number =30−12=18=30-12=18. Using 5!/2!5!/2! ignores the repeated L, and 3030 ignores the restriction.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake