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JEE Main 2017 · Mathematics · Permutations and Combinations · medium

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

Single correct option

The number of arrangements of all the letters of the word MISSISSIPPI in which no two S's are adjacent is
  1. A. 36753675
  2. B. 73507350
  3. C. 3465034650
  4. D. 58805880
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Answer: (B) 73507350

First arrange the other 77 letters M, I, I, I, I, P, P (four I's and two P's): 7!4! 2!=105\dfrac{7!}{4!\,2!}=105 ways. These create 88 gaps (including both ends). Place the four S's in distinct gaps, so no two are adjacent: (84)=70\binom84=70 ways. Total =105×70=7350=105\times70=7350. Using (74)=35\binom74=35 gaps by mistake gives 36753675, and ignoring the restriction gives 3465034650.
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Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake