Originally Posted by gt_croz
I've always seen the number that Waffle House quotes, but I can't seem to reproduce that high a number.
Here's a PDF to an older version of their menu. It's missing one option on the hash browns that they offer now, mushrooms. You can get them "capped" with shrooms now.
http://www.wafflehouse.com/whmenu.pdf
So, the choices are:
Scattered on the grill
Covered with cheese
Chunked with ham
Topped with chilli
Diced with tomatoes
Peppered with peppers
Capped with Mushrooms
If you look it as a binary operation (the topping is either ON or OFF), with 6 different possible options (Scattered comes by default) than you have a 6 digit binary number, or 2 to the 6th power = 64 different combinations. If you factor in 3 different sizes, then you'll have a total of 192 possiblities.
Maybe it's not such a coincidence that three flyers order their hash browns the same way.
That number they quote must take into account every other item on the menu.
OK so this is off topic, oh well.
I found this excerpt on someone's blog at
http://www.livejournal.com/~honeyspy/246405.html
I have no idea if this is correct. Any actuaries (Bruce are you still out there?) or other mathmaticians care to comment.
"ok... I got 765 combinations. that doesnt account for things like if someone wanted double of any one topping because if you allow for that, then theoretically it is infinite. if I set it up right, and I think I did, it's like this:
you can have 1 combination where you have all 8 toppings, and 8 where you just have a single topping. to that, you add the following (pardon the notation):
8C7+8C6+8C5+8C4+8C3+8C2
now, since you can have single double or triple orders, you have to multiply this all by 3. so you end up with:
3(9+8C7+8C6+8C5+8C4+8C3+8C2) and I think that that equals 765."