What is the permutation of word "MISSISSIPPI"? [duplicate]

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What is the total no. of permutations of the letters of the word MISSISSIPPI in which no four "I"s come together?

My try-: $7!/4!\times 2! \times 8!/4!$

But not getting the right answer.

Please help

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2 Answers

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Number of permutations of the word MISSISSIPPI in which no $I$'s are together =Number of permutations of the word MISSISSIPPI-Number of permutations in which $4$ I's are always together

$\dfrac{11!}{4!2!4!}-\dfrac{8!}{2!4!}$

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Just put all the i's together.

Total number of permutations =$\dfrac{11!}{4!2!4!}$. and total number of permutations in which all i's are together=$\dfrac{8!}{2!4!}$.

Just subtract and get the answer.

i.e$\dfrac{11!}{4!2!4!}-\dfrac{8!}{2!4!}$.

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