How many ways to build a hamburger?

Question

Friendly's recent advertising campaign claims there are over 10 trillion combinations of hamburgers. Their options are: Protein (4) Bread (5) Cheese (7) Premium topping (3) Hot toppings (10) Cold toppings (8) Sauces (11)

Their calculation is (4)x(5)x(2^7)x(2^3)x(2^10)x(2^8)x(2^11)=10,995,116,277,760

I think it should be 4x5x7x3x10x8x11=369,600

Thoughts?

No. There's just one way. If you do it wrong, the hamburger is ruined... — Asaf Karagila, May 03 '13 at 02:23
Their definition of a hamburger is that it must have exactly one protein and exactly one bread, but any number of the other options. — Austin Mohr, May 03 '13 at 02:24
@Dan: Welcome to MSE! It really helps to format questions using Mathjax (see FAQ). Regards — Amzoti, May 03 '13 at 02:39

score 2 · Accepted Answer · answered May 03 '13 at 02:23

2

Their calculation is assuming you can put any number of cheeses/toppings/sauces on your burger, not just one of each.

To elaborate, think about this in binary. If you have $7$ possible cheeses, this corresponds to a bit-string of length $7$. For example, not having any cheese can be written as:

$$0000000$$

while having the first and third types of cheese can be written as

$$1010000.$$

There are $2^7$ possible cheese strings.

In general, when there are $n$ choices, there are $2^n$ possible combinations.

answered May 03 '13 at 02:23

parsiad

25,154

That makes sense. It has been a long time since Stats class in college, so it's a little rusty...ok, a lot rusty! Thanks. – Dan May 03 '13 at 02:31
@Dan This is combinatorics, not statistics! – Alex Provost May 03 '13 at 02:51

How many ways to build a hamburger?

1 Answers1