Lesson An Introduction to Permutations

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About BrittanyM: Math is my hobby, my passion, my life.

Hello everyone!

Today we will be discussing permutations.  This is an area which all algebra students will study at some time, and because of its many practical uses, we should all revisit such a lesson from time to time.

In problems concerning arrangement and order, permutation is a must.

First, let's review the permutation formula:
{{{n!/(n - r)!}}}
Where "n" is the total number of items and "r" is the number of these items taken from "n".

If you're new to permutations, this may be the first time that you've seen an exclamation point used in math.  
For example, 4! is nothing more than simplified notation for 4 x 3 x 2 x 1.  It's just used to make notation more managable when the figures get large nad unwieldly.

Permutation has virtually unlimited uses.  It can be used to identify anything from seating arrangements to placement of numbers in an ID set.

Let's go over some examples.

In how many different ways can four puppies be arranged in a line?

4!
24

In how many different ways can five students be seated from a set of eight?

{{{8!/(8-5)!}}}
6720

Now, let's try something a bit different.
How many different letter combinations can be made from the word MATH?

4!
24

One last example:
From the word TRIGONOMETRY,how many different letter combinations can be made?
(This one is a bit trickier.  Since there are letters that are repeated and thus indistinguishable, we will have to deduct them from the total).

{{{12!/2! 2! 2!}}}
59875200

Now that we have a better understanding of permutations, solving problems like the ones above is much less painful.  While they could each be solved using different methods by hand, I'm sure that we all have far greater things to do with our time.  :)