Question 842956
How many different words can be formed using all the letters of the word MISSISSIPPI?<pre>If they were all distinguishable, the answer would be 11!.
But since the 4 I's are indistinguishable we must divide by 4!,
and since the 4 S's are indistinguishable we must also divide by 4! again,
and since the 2 P's are indistinguishable we must also divide by 2!

Answer: {{{11!/(4!4!2!)}}} = {{{39916800/(24*24*2)}}} = {{{39916800/1152}}} = {{{34650}}}</pre>In how many of these permutations do the four 'I's not come together?<pre>We must subtract all the ways the I's come together.

That's the distinguishable arrangements of these 8 "things"

(IIII),M,S,S,S,S,P,P

If they were all distinguishable, the answer would be 8!.
But since the 4 S's are indistinguishable we must divide by 4!,
and since the 2 P's are indistinguishable we must also divide by 2!

So we must subtract {{{8!/(4!2!)}}} = {{{40320/(24*2)}}} = {{{40320/48}}} = {{{840}}}

So we subtract the 840 ways the I's come together from the {{{34650}}} and
get {{{33810}}} 

Edwin</pre>