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JEE Main 2019
Permutations & Combinations
Permutations and Combinations
Medium

Question

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

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Solution

Key Concept: The Gap Method for "No Two Adjacent" Restrictions

This problem involves forming words from a given set of letters with a specific restriction: no two 'S's can be adjacent. The most effective strategy for such problems is the Gap Method. The core idea of the Gap Method is:

  1. First, arrange the items that are not restricted (the items that can be adjacent).
  2. These arranged items create "gaps" (including at the ends) where the restricted items can be placed.
  3. Place the restricted items into these gaps, ensuring that no two restricted items are placed in adjacent gaps (or in the same gap), thereby satisfying the "no two adjacent" condition.

**Step-by-Step

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