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!