Multiple choice

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

  1. 6. 7. $^8 C_4$
  2. 6. 8. $^7 C_4$
  3. 7. $^6C_4. ^8 C_4$
  4. 8. $^6C_4. ^7 C_4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First arrange the 7 non-S letters, giving 7!/(4! x 2!) arrangements. These letters create 8 gaps, and choosing 4 gaps for the S letters ensures that no two S letters are adjacent, giving 7!/(4! x 2!) x C(8,4).

AI explanation

To ensure no two S letters are adjacent in MISSISSIPPI, we first arrange the 7 remaining letters (M, I, I, I, I, P, P), which can be done in 7! / (4! * 2!) = 105 ways. Arranging these 7 letters creates 8 gaps (including the ends) where the 4 S letters can be safely placed to keep them apart. The 4 S letters can be chosen and placed in these 8 gaps in 8C4 ways, giving a total of 7! / (4! * 2!) * 8C4, which simplifies to 7 * 6C4 * 8C4.

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