Exercise 1.14

Question

You are ordering two pizzas. A pizza can be small, medium, large, or extra large, with
any combination of 8 possible toppings (getting no toppings is allowed, as is getting all
8). How many possibilities are there for your two pizzas?

fifthist x · Accepted Answer

There are $4$ choices for sizes and $8$ choices for toppings, of which any
combination (including no toppings) can be selected.

The total number of possible choices of toppings is $\sum_{i=0}^{8}\binom{8}
{i} = 2^8 = 256$. Thus, the total number of possible size-topping combinations
is $4 * 256 = 1024$.

We wish to sample two pizzas, with replacement, out of the $1024$ possibilities.
By Einstein-Bose, there are a total of $\binom{1025}{2}$ choices.

Exercise 1.14

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Exercise 1.14

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