Friday, July 20, 2018

Permutations

Permutations have always interested me. Ever since I was a baby mathematician bouncing on my dad's knee, I liked permutations. That's even if I didn't know that was what they were called.

Later I learned the big word and its meaning. The mathematical term is defined as the act of arranging all the members of a set into some sequence or order. The number of unique permutations of a given set of size n = n! called “n factorial” which is the product of 1, 2, 3, …, n of the terms. The exclamation sign is the symbol for this mathematical operation.

For example, the number of permutations of a set with four members is

4! = 1 x 2 x 3 x 4 = 24.

There are 24 unique ways (or orders) that four members of a set could be arranged.

Permutations and partial permutations (sub sets with less members than the overall set) are very important in certain math areas such as statistics. (I’ll keep it simple and not address partial permutations. Fell free to google it and learn more.)

I said permutations have always interested me. Growing up there was a beer brewed in nearby Great Falls, Montana called “Great Falls Select.” I don’t know if it is still available or not. I sort of imagined a big pipe stuck in the Missouri River where it flows through Great Falls that goes to the brewery. Not exactly Coors “Rocky Mountain Spring Water,” but probably not that different.

Their motto was “Always Brewed Carefully.” The neat thing about the phrase is that all permutations make sense and they used them all in their ads. Notice you can abbreviate the three words as “A,” “B,” “C.” Isn’t that elementary? Good advertisement copy!

Since there are three terms, then the number of possible permutations is

3! = 1 x 2 x 3 = 6.

Here they are:

A B C
A C B
B A C
B C A
C A B
C B A

Let’s try the permutations to see if they all make sense:

Great Falls Select is

ABC = Always Brewed Carefully
ACB = Always Carefully Brewed
BAC = Brewed Always Carefully
BCA = Brewed Carefully Always
CAB = Carefully Always Brewed
CBA = Carefully Brewed Always

Maybe that’s where I got my love of math … from beer!!

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