Find the number of ways to arrange the letters of the word $\text{MISSISSIPPI}$ such that no two $\text{I}$'s are together.

Solution

1. The word MISSISSIPPI contains 11 letters: 1 M, 4 I's, 4 S's, and 2 P's.
2. Arrange the remaining 7 letters (M, S, S, S, S, P, P) in $\frac{7!}{4!2!1!}=105$ ways.
3. Create 8 possible gaps around these 7 letters to place the 4 I's, which can be done in $\left(\genfrac{}{}{0ex}{}{8}{4}\right)=70$ ways.
4. Calculate the total arrangements by multiplying the results: $105\times 70=7350$.
5. Hence the answer is (A).