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NDA 2022 Maths · Mathematics · Permutations and Combinations · hard

The number of arrangements of the letters of SUCCESS in which no two S's are adjacent is

Single correct option

The number of arrangements of the letters of SUCCESS in which no two S's are adjacent is
  1. A. 120120
  2. B. 420420
  3. C. 6060
  4. D. 240240
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Answer: (A) 120120

Arrange U, C, C, E first: 4!2!=12\frac{4!}{2!}=12 ways. This creates 55 gaps; choose 33 of them for the S's: (53)=10\binom53=10. Total 12×10=12012\times10=120. The value 420420 is the unrestricted count.
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Original question written in the NDA 2022 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