Q. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?
A) $7.{\ ^{6}C}_{4}.{\ ^{8}C}_{4}$
B) $8.{\ ^{6}C}_{4}.{\ ^{7}C}_{4}$
C) $6.7.{\ ^{8}C}_{4}$
D) $6.\ 8.{\ ^{7}C}_{4}$
Explanation
(a)
Given word is MISSISSIPPI
Here, I=4 times, S=4 times, P=2 times, M=1 time
_M_I_I_I_I_P_P_
Required number of words $= \ ^{8}C_{4} \times \frac{7!}{4!2!}$
$= \ ^{8}C_{4} \times \frac{7 \times 6!}{4!2!} = 7.\ \ ^{8}C_{4}.\ ^{6}C_{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.