# Anagrams Question [duplicate]

How many anagrams of the word mississippi are there that have at least two consecutive i’s? My approach was: Finding the total amount of anagrams (11! / 4! 4! 2!). And then to calculate the amount of options without 2 consecutive i's. In the end, to find the difference between them. However, the result felt me to big intuitively. Do I miss something?

Thanks

## marked as duplicate by polfosol, Yanior Weg, ThorWittich, Adrian Keister, G-manSep 17 at 1:05

• Well, you have a typo. You mean ${11!\over 4!4!2!}$ Is this what's making your answer too big? – saulspatz Sep 15 at 18:14
• You are correct. it's 4!4!2!. Editing – Bob_Bobb Sep 15 at 18:54

There is a way to do this, actually.

First, order the letters MSSSSPP. This can be done in $$\displaystyle \frac{7!}{4!2!}=105$$ ways.

Now, you have $$8$$ spaces between those letters to possibly insert I's (ends included).

Now, choose $$4$$ of those $$8$$ spaces to insert an $$I$$.

This gives a total of $$105\cdot 70=7350$$ ways.

Now, we are looking for the complement, so our answer is $$\displaystyle \frac{11!}{4!4!2!}-7350=34650-7350=27300$$ ways.

• Thanks! Great explanation! – Bob_Bobb Sep 15 at 18:57