05.05.2019: Permutations and Combinations, 3/5: Permutations Involving Identical Objects

Today's soundtrack is Hellyeah: Band of Brothers, an awesome southern groove metal album from the American supergroup that features the legendary Vinnie Paul on drums.

Today, I'm learning how to calculate the permutations of a series that includes identical objects.

If I have five Smarties and I want to see how many ways I can arrange them by colour, I'd of course calculate 5!, which is 120. But what if two of them are blue? I don't want to count the same kind of arrangement twice. I'd then calculate 5!/2!, giving me 5⋅4⋅3, which is 60. But what if two of the non-blue Smarties are red? Well, I'd calculate 5!/2!2!, which is 30.

One important thing to note is that if using a calculator for this kind of equation, any factorials that are multiplied together must be placed inside brackets to avoid calculation errors.

The general formula of this concept is as follows:

"If there are n objects in which there are a objects of one type, b objects of another type, c objects of another, and so on, then the number of permutations is n! / a!b!c!..." (contentconnections.ca).

That's it for today. Next time, we'll be looking at combinations!