too. many. options.

Last night to our surprise, we received a box from Will's sister, Kate. It contained our Christmas and birthday presents. We were happy to get the presents but we would have been happier had Kate been feeling better and not on call so we could have seen her more at Christmas.

Our big present was that each of us got a gift certificate to Timbuk 2. There are many things you can get from Timbuk 2 but the coolest is that you can design your own bag using their bag builder and they will make it for you just how you want it. Super cool.

Will's pretty much got his figured out. He's already got a small messenger so he went for the medium. A little maroon here and there. And he's about finished.

As for myself - I'm somewhat drowning in the options. I've picked my bag:

A small messenger

But here's why I'm drowning in options (and why I'm a nerd as you'll see in a second):

The menu to build the bag.

As you can see there's a myriad of options.

Now on to why I'm a nerd. I wanted to know how many possibilities there were.

So, I first had to remind myself of the difference between a permutation and a combination. In a permutation order "matters" but in a combination it doesn't.

So if your set is {C,A,T} and you have to pick 2; your permutations are {CA, CT, AC, AT, TC, TA} and your combinations are {CA, AT, CT}.

It matters which panel is which color; hence, it's a permutation. But none of this accounts for being able to reuse an element of the set. That's math I didn't look up.

I then had to look up to remind myself how to determine how many permutations could be made from a set - n!/(n-m)! where n is the number of elements, in this case colors and fabrics, in the set and m is how many are being chosen, 3 - one for each panel. For combinations it's: n!/(m!(n-m)!).

So here's exactly just how many options there are (not accounting for reuse):

Holy COW!

And that's just for the 3 panels, not to mention the logo (32 colors) and lining (10 colors) choices!

Anyone want to offer up some suggestions on the bag? Or more info on the math?

P.S. if you do, here are the colors I don't like: flame, gold, orange, burnt orange, citron, purple, light green, rusty, army, lavender, and hot pink.