Question

Help me Pls

Answer 1

So there are 8 ways to have the meat.

The topping is tricky; each of the seven toppings is there or not so 2^(7) of those.

I think sauces is likewise to be 2^(4) though it was written oddly.

Answer 2

The way you state the problem is a little confusing.

Are there four different basic kinds of burgers? (Like, maybe, beef, pork, chicken, and veggie?)

OR

Is there just one basic kind of burger and you are going to make four orders with different specs?

Answer 3

(# of pattie options) \* (# of topping options) \* (# of sauce options) \* (# of onion ring options)

Now think through each term one at a time.

The pattie can either be 1 or 2. So # of pattie options = 2.

The topping options are either 0, or the 7 single options, or the 7C2 = 21 combinations of 2, or the 7C3 combinations of 3, or ...

The short answer to that is that it's the number of subsets of a set with 7 elements, including the empty set (no topping) or the whole set (all 7 toppings).

That is, if you write the 7 toppings as a set of 7 elements, the possible options are all the subsets of that set.

Do you know how to calculate the number of subsets of a set?

Can you see now how to calculate the number of sauce options and the number of onion ring options?