Question

How many different words can be fanned by jumbling the letters of the word MISSISSIPPI in which no two 's' are adjacent

• A. $7{\cdot }^6{C}_2{\cdot }^8{C}_4$
• B. $6\cdot 7{\cdot }^8{C}_4$
• C. $6\cdot 8{\cdot }^7{C}_4$
• D. $8{\cdot }^6{C}_4{\cdot }^7{C}_4$

Answer 1

Answer: (A)

$7{\cdot }^6{C}_2{\cdot }^8{C}_4$

Total letters $=11M=1,S=4,P=2,I=4$

first we arrange the letters other than $S($ i,e. $M,P,P,l,I,I,I)$

$\therefore$ No. of such arrangements are $=\frac{7!}{4!2!}$

$\therefore -M-P-P-I-I-I-I-.....(\ast )$
Now, we place $4S$ in the blank places, which can be done by ${}^8{C}_4$ ways,

because there are $8$ blank places in $(\ast )$

$\therefore$ Required no.of ways are $=\frac{7!}{4!2!}{\times }^8{C}_4=7\times \frac{6!}{4!2!}{\times }^8{C}_4$
$=7{\times }^6{C}_2{\times }^8{C}_4$