# How many ways are there to arrange the letters in the word “mississippi” such that all “p” precede all “i”?

How many ways are there to arrange the letters in the word "mississippi" such that all "p" precedes all "i"?

My possible solution:

Consider: p p _ _ _ _ _ _ _ _ _ so 9! ways to arrange words(?)

follwed by: p _ p _ _ _ _ _ _ _ _ where i must not be in between both "p". So 9! / (something)(?).

and so on. But it obviously is infintely loooong process. Am i on right track? And what is a possible general solution to this problem?

• Certainly not infinitely long, but there are better ways. – Matt Samuel Mar 3 '16 at 21:00

Choose 6 positions to contain the p's and i's. They must be arranged ppiiii. There are $\binom{11}6$ ways to do this. In the five remaining spaces, choose 4 spots to put s in. There are $\binom54$ ways to do this. Then the m can only go in one place.