How many different ways could a guest on the show have topped his/her taco?

Question

I love to watch cooking shows. Last week the show was about tacos and the chef had little dishes with three different toppings for the tacos: grated cheese, guacamole, and salsa.

Answer 1

What you're basically asking is, how many subsets are there of a set that has 3 members.

 

The answer depends slightly on whether you include no topping at all as one of the ways.

 

Any finite set of N elements has 2^N different subsets, which includes the null set ( {} ) as one of them.  So if you include "no toppings" as one of the possibilities, then the answer is 2³ = 8.  If you don't, then you have to subtract 1.

 

By the way, this has a name.  The set of all subsets of a set is called the "power set" of that set.

 

Answer 2

Three toppings A B C which can be valued 1 - ON or 0-Off

2^3 = 8