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# How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent.

$\begin{array}{1 1}(A)\;8.6C_4.7C_4\\(B)\;6.7.8C_4\\(C)\;6.8.7C_4\\(D)\;7.6C_4.8C_4\end{array}$

Toolbox:
• $C(n,r)=\large\frac{n!}{r!(n-r)!}$
• $n!=n(n-1)(n-2)(n-3)......(3)(2)(1)$
Given wird is MISSISSIPPI
Here I=4 times,S=4 times,P=2 times,M=1 time
$\therefore$ Required number of words =$8C_4\times \large\frac{7!}{4!2!}$
$\Rightarrow 8C_4\times \large\frac{7\times 6!}{4!2!}$
$\Rightarrow 7.8C_4.6C_4$
Hence (D) is the correct answer.

+1 vote