Domino's Advertising Pizza Claim

Question

I just got a Dominos promotional flier through the post and one of the graphics advertising 'create your own pizza' lists the various toppings and claims there are 'more combinations than people in the world'

There are 19 toppings available, I am interested to know how you work it out.

Answer 1

For each topping, you can either include it or not, so $$ 2^{19}=524,288 $$ which is considerably less than the population of the world.

Answer 2

There are 19 toppings and 4 different crusts, HOWEVER you are also allowed pizzas where you choose each half. Therefore its,

$$2^{19}\times 4 + {2^{19}\times 4 \choose 2}$$

I would guess this is larger than 7 billion.