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Q.
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two $S$ are adjacent?
Permutations and Combinations
Solution:
We can permute $M, I, I, I, I, P, P$ in $\frac{7 !}{4 ! 2 !}$ ways. Corresponding to each arrangement of these seven letters, we have 8 places where $S$ can be arranged as shown below with $X$.
$X \square X \square X \square X \square X \square X \square X \square$
We can choose 4 places out of 8 in ${ }^8 C_4$ ways. Thus, the required number of ways
$=\left({ }^8 C_4\right)\left(\frac{7 !}{4 ! 2 !}\right)=(7)\left({ }^8 C_4\right)\left({ }^6 C_4\right)$