So now that we’ve covered factorials just thought I’d go a little into what we can do with them.  And I even thought of any example to do it without pimping out my books.  I’ll try.  Now say we get to choose to go to Bermuda, Bahamas, Key Largo, Montego, and whatever the fifth place in that Kokomo song is over two day, but we can go only to one place one day and we cannot go to the same place twice.  So we can chose 2 out of 5 combinations or 5 ‘chose’ 2.  Got it? So, let me denote each place we can visit as BE, BA, KL, MO, and whatever the fifth place is.  Oh wait … it’s Kokomo!  Thank you, Metro Lyrics!  Okay, that one we can denote as KO then.   The total number of combinations of places we can visit is (BE,BA) + (BE,KL) + (BE,MO) + (BE, KO) + (BA,KL) + (BA,MO) + (BA, KO) + (KL,MO) + (KL,KO) + (MO, KO) = 10.

Now, look at this.

Eh?  Eh?  What did I tell ya?  We basically could do the same calculation using factorials.  Which might be useful if we want to increase our number of places to 10 or 20 or 50 or even more.  Otherwise, we could end up summing up millions of terms, but let’s be real — who wants that?  Or like if Tina is going through a grad school catalogue and wants to choose two from the thirty-something areas of study like she might in this fourth book I might write.  What?  I’m not talking about my trilogy!  I’m talking about a fourth … okay, I’ll stop.  But yeah, that’s basically how we can do combinations with factorials.  But join me next time as I talk about sampling without replacement as opposed to sampling with replacement such as bootstrapping, which we will cover even later. And speaking of bootstrapping …

There you go.  Happy Friday!  Unless you’re not reading this on a Friday — then it’s Happy Day other than Friday!