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In how many of the distinct permutations...

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?

Text Solution

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There are 4I, 4S,2P and 1M in the word 'MISSISSIPPI'.
Total number of words using all letters
`= (11!)/(4!4!2!) = 34650`
If 4T' are together then taking them as one letter, number of words using 8 letters (in which 4S and 2P are there)`=(8!)/(4!2!) = 840`
Therefore, the number of words in which 4T' are not together `= 34650 - 840 = 33810`
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