The Mississippi Counting Problems

Today I’m continuing to talk about the fundamentals of combinatorics with the Multinomial Theorem, and what better way to do this than to tackle some classic combinatorics problems 😉

Have you got the chops to solve these problems?

The Mississippi Counting Problems

Problem 1

How many total arrangements of the letters in MISSISSIPPI are there?

Problem 2

How many arrangements of the letters in MISSISSIPPI exist such that the 2 P’s are separated?

Problem 3

How many arrangements of the letters in MISSISSIPPI have at least 2 adjacent S’s?

Note:

If you need a review of the basics, check out this intro to combinatorics post:

Solution #1: Permutations of MISSISSIPPI

In the last post we discovered that we can find the number of unique permutations by using the Fundamental Theorem of Counting.

Since MISSISSIPPI has 11 letters, draw eleven lines and fill each in with the number of available letter choices, e.g. 11 options for the first, 10 for the second, and so on…

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