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

Total number of letters in MISSISSIPPI

    \[=\text{11}\]

Letter Number of occurrence

⇒ Number of permutations =
NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Image 21

We take that 4 I's come together, and they are treated as 1 letter,

∴ Total number of letters

    \[=11\text{ }-\text{ }4\text{ }+\text{ }1\text{ }=\text{ }8\]

⇒ Number of permutations =
NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Image 22

Therefore, total number of permutations where four I’s don’t come together

    \[=\text{ }34650-840=33810\]