Combinations galore

Combinations. They are taught in math as a prelude to probability. How many of these times how many of those equals this many to choose from.

We normally give examples in clothing - 3 pairs of pants, 5 shirts, 2 kinds of shoes and 3 hats.
How many combinations can you make?

3 x 5 x 2 x 3 = 90

But I saw an article about a new hamburger chain in town that offers 321,120 combinations!

As I often tell my wife, more choices aren't always a good thing.

Here's the menu from the website of the burger place, in case you are already hungry. (looks suspiciously veggie to me)

Step 1 Meat choice = 4 x 3 x 3 = 36 variations choose 1
Step 2 Cheese = 12 variations choose 1
Step 3 Toppings = 30 variations choose 4
Step 4 Sauce = 21 variations choose 1
Step 5 Bun = 3 variations choose 1 IF you chose a bun in Step 1

36 x 12 x 21 x 3 = 27,217 choices WITHOUT getting into the toppings.

Since we have to choose 4 out of 30 (including premium priced ones) we have a LOT of choices.

If we divide 321,120 (their number) by 27,217 (our number) to get 11.8 which in not the number of topping choices, but it is about what the burger will cost you in dollars.

Math can't solve this without knowing more about the assumptions of the newspaper writer and the actual menu at the restaurant!