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

Question

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent ? (A) 8⋅ 6C4⋅ 7C4 (B) 6⋅ 7 ⋅ 8C4 (C) 6⋅ 8⋅ 7C4 (D) 7⋅ 6C4⋅ 8C4

Tardigrade Admin · Accepted Answer

First of all arrange M, I, I, I, I, P, P This can be done in (7 !/4 ! 2 !) ways. × M × I× I× I× I× P× P× If we place is S at any of the X places then no two Sâs are together. ∴ total number of ways =(7 !/4 ! 2 !)⋅8C4 =7× 6C4× 8C4 ways.

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

$8 \cdot^{6} C_{4} \cdot^{7} C_{4}$

$6 \cdot 7 \cdot^{8} C_{4}$

$6 \cdot 8 \cdot^{7} C_{4}$

$7 \cdot^{6} C_{4} \cdot^{8} C_{4}$

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

8⋅6C4​⋅7C4​

6⋅7⋅8C4​

6⋅8⋅7C4​

7⋅6C4​⋅8C4​

First of all arrange M,I,I,I,I,P,P This can be done in 4!2!7!​ ways. ×M×I×I×I×I×P×P× If we place is S at any of the X places then no two S’s are together. ∴ total number of ways =4!2!7!​⋅8C4​ =7×6C4​×8C4​ ways.

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

$8 \cdot^{6} C_{4} \cdot^{7} C_{4}$

$6 \cdot 7 \cdot^{8} C_{4}$

$6 \cdot 8 \cdot^{7} C_{4}$

$7 \cdot^{6} C_{4} \cdot^{8} C_{4}$