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?

  • $\begingroup$ Certainly not infinitely long, but there are better ways. $\endgroup$ – 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.


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