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

  • 8 . 6C4 . 7C4

  • 6 . 7 . 8C4

  • 6 . 8 . 7C4

  • 7 . 6C4 . 8C4

Answer

D.

7 . 6C4 . 8C4

Other than S, seven letters M, I, I, I, P, P, I can be arranged in 7!/2! 4!=7 . 5 . 3.
Now four S can be placed in 8 spaces in 8 C4 ways. Desired number of ways = 7 . 5 . 3 . 8C4 = 7 . 6C4 . 8C4.

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