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!