Just wondering how you would solve this problem? Are there multiple ways to do so (besides the combonation rule? Why does it work? Pine Pizza Palace sells pizza plain or with one or more of the following toppings: pepperoni, sausage, mushrooms, olives,onions, or anchovies. (six toppings or plain) How many different pizzas can be made? (Hint: A person can select or not select each item.) I think that the answer is 64 but why? How many different ways could I go about getting that answers?
Think of a 6-bit binary number. Each bit represents a topping. every binary number from 000000 (zero) to 111111 (63) inclusive indicates a possible pizza. You could also add up C(6,0), C(6,1), C(6,2) . . . Where C(6,n) is the combination of 6 objects taken n at a time. C(6,n) = 6! / n!(n-1)!
Another way which is equivalent to the binary string: For each of the 6 toppings you have two choices - to use it or to not. So for just pepperoni, there are 2 different pizzas to make - pep and plain. For pepperoni and sausage, there are 2*2 pizzas - pep & saus, pep, saus, and cheese. For three toppings, there are 2*2*2 pizzas. Follow? Note that this only works when each event (ie. topping) is independent of the others. Say for some reason you can only add sausage if you add pepperoni (in other terms, the sausage event depends on the pepperoni event). You won't have 2*2 different pizzas this time, since sausage pizza is not possible.
