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.)
six toppings means that there are 2^6=64 ways to select them or not.
number of subsets of 6 elements
= 2^6
= 64
which includes the nullset (plain pizza) and all elements ("the works")
To calculate the number of different pizzas that can be made, we need to consider the choices for each topping.
Since there are 6 toppings available (pepperoni, sausage, mushrooms, olives, onions, and anchovies), there are two possibilities for each topping: selecting it or not selecting it.
For each topping, there are 2 choices: either select it or not select it. Since we have 6 toppings, this gives us 2^6 = 64 possible combinations.
However, we also need to consider the plain pizza option, which is an additional choice. So the total number of different pizzas that can be made is 64 + 1 = 65.
To find the number of different pizzas that can be made, we need to consider the choices for each topping.
For each topping, a person can either select it or not select it. Since there are 6 toppings that can be added or omitted, each with 2 options, we can use the concept of combinations to find the total number of different pizzas.
To calculate this, we can use the formula for combinations:
Total combinations = 2^n
where n is the number of options (in this case, 6 toppings).
Therefore, the total number of different pizzas that can be made is:
Total combinations = 2^6 = 64
So, there are 64 different pizzas that can be made at Pine Pizza Palace.