how many different word can be formed by jumbling the letter of the word
MISSISSIPPI in which no three $"S"$ occur together
No. of arrangement of the words MISSISSIPPI is $ = \frac{11!}{4!\cdot 4!\cdot 2!}$
now arrangement of the words in which all $ "S"$ are together is $ = \frac{8!}{4!\cdot 2!}$
total no. of arrangements of the words in which all four $"S"$ are occur together is $ = \frac{11!}{4!\cdot 4!\cdot 2!}-\frac{8!}{4!\cdot 2!}$
i want be able to go further , could some help me with this, Thanks
Best Answer
All arrangements : $11!/(4! 4! 2!)=34650$
4s together : $8!/4!2!=840 $
3s together 1s apart : $ 56*7!/(4!2!)=5880$
[When $3s=X$ is at the beginnining or at the end $14*7!/(4!2!)$ cases and if not $42*7!/(4!2!)$ cases]
which gives you $27930$ cases ..