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  • How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two are adjacent?<div

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

Option: 1

(8)\left({ }^{\circ} C_{4}\right)\left({ }^{7} C_{4}\right)


Option: 2

(6) (7) \left({ }^{8} C_{4}\right)


Option: 3

(6)(8)\left({ }^{7} C_{4}\right)


Option: 4

(7)\left({ }^{6} C_{4}\right)\left({ }^{8} C_{4}\right)


Answers (1)

best_answer

 We can permute \mathrm{M, I, I, I, I, P, P} in \mathrm{\frac{7 !}{4 ! 2 !}} ways.

Corresponding to each arrangement of these seven letters, we have 8 places where \mathrm{s} can be arranged as shown below with \mathrm{X}.
\mathrm{X\, \square \, X\, \square\, X \, \square\, X\, \square \, X \, \square X\, \square \, X \, \square}

We can choose 4 places out of 8 in \mathrm{{ }^{8} C_{4}} ways. Thus, the required number of ways

\mathrm{=\left({ }^{8} C_{4}\right)\left(\frac{7 !}{4 ! 2 !}\right)=(7)\left({ }^{8} C_{4}\right)\left({ }^{6} C_{4}\right)}

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HARSH KANKARIA

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