Question

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

• A. $8{\times }^6{C}_4\times 7$
• B. $6{\times }^6{C_4\times }^8{C}_4$
• C. $6{\times }^6{C_4\times }^7{C}_4$
• D. $7{\times }^6{C_4\times }^8{C}_4$

Answer 1

Answer: (A)

$8{\times }^6{C}_4\times 7$

$MISSISSIPPI$

$M-1$

$S-4$

$I-4$

$P-2$

For all 'S' seperate using gap method

$M,I,P\to 7$

$\left(\frac{7!}{4!2!}\right)\to$ arrangement of all Alphabet it creates 8 gaps.

$\underset{selectionof4gaps}{\underset{\downarrow }{8C_4}}$ $\underset{arrangementof4s^{\prime }}{\underset{\downarrow }{\left(1\right)}}$ $\frac{7!}{4!2!}=8_{C_4}.7.6_{C_4}$