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

Question

Smart Achievers · Accepted Answer

(1)

Leaving S, we have 7 letters $M, I, I, I, P, P, I$

Ways of arranging them $= \frac{7!}{2! 4!} = 7 \cdot 5 \cdot 3$

And four S can be put in 8 places in ${}^{8}C_{4}$ ways.

Therefore, the required number of ways is $= 7 \cdot 5 \cdot 3 \cdot {}^{8}C_{4} = 7 \cdot {}^{6}C_{4} \cdot {}^{8}C_{4}$

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