Combinatorics – MISSISSIPPI Combinations with Separated S’s

combinatoricsprobability

How many combinations are there to arrange the letters in MISSISSIPPI requiring that the 2 S's must be separated?

I found there are 34650 combinations to arrange without restriction.

How to approach this question?

Best Answer

We know that the string will take the form of

$$*S█S█S█S*$$

where $█$ MUST have at least one character and $*$ can be of any length (even 0). I would suggest the following steps:

  1. Find the number of ways you can put the $S$s (they can be in positions $(1,3,5,7)$, $(2,5,8,11)$, $(1,4,6,9)$, etc.)
  2. Find the number of different strings you can make with $MIIIPPI$ (that's $MISSISSIPPI$ without the $S$s)
  3. Multiply the two.

I leave the math for you to do.

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