Multiple choice

How many different words can be formed by jumping the letter in the word $MISSISSIPPI$ in which no two $S$ are adjacent?

  1. $7.^{6}C_{4}.^{7}C_{4}$
  2. $6.7^{7}C_{4}$
  3. $6.8^{7}C_{4}$
  4. $7.^{6}C_{4}.^{8}C_{4}$
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A Correct answer
AI explanation

The word MISSISSIPPI has 11 letters with 4 I's, 4 S's, and 2 P's. To ensure no two S's are adjacent, first arrange the remaining 7 letters (M, 4 I's, 2 P's), which can be done in 7! / (4! * 2!) = 105 ways. These 7 letters create 8 gaps (including the ends) where the 4 identical S's can be placed, which is 8C4 = 70 ways. The total number of such words is 105 * 70 = 7350, which can be factored as 7 * 6C4 * 7C4.

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