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?
Options
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:
- First, arrange the items that are not restricted (the items that can be adjacent).
- These arranged items create "gaps" (including at the ends) where the restricted items can be placed.
- 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