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

Letters in MISSISSIPPI: M(1), I(4), S(4), P(2). Total = 11 letters.First, arrange the letters other than S: M, I, I, I, I, P, P.Number of letters = 7.Ways to arrange them = $\frac{7!}{4!2!}=\frac{7\times 6\times 5}{2}=105$.Now, there are 8 possible spaces (including ends) to place the 4 S's so that no two are adjacent.Ways to choose spaces for S = ${}^8{C}_4$.Total ways $=\frac{7!}{4!2!}\times {}^8{C}_4=105\times {}^8{C}_4$.Check the options:Option D: $7\cdot {}^6{C}_4\cdot {}^8{C}_4=7\cdot \frac{6\cdot 5}{2}\cdot {}^8{C}_4=7\cdot 15\cdot {}^8{C}_4=105\cdot {}^8{C}_4$.This matches.