If a pizza could have some (or none) toppings out of cheese, pepperoni, ham, sausage, mushrooms, and pineapple. How many different kinds of such pizzas can be made? Assume order of toppings does not matter and assume for each topping you can have none, normal, or extra of such topping.

Question

Mathematics

Lyric Melton

1 March, 00:05

If a pizza could have some (or none) toppings out of cheese, pepperoni, ham, sausage, mushrooms, and pineapple. How many different kinds of such pizzas can be made? Assume order of toppings does not matter and assume for each topping you can have none, normal, or extra of such topping.

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Leonard Harding · Answer 1

721

Step-by-step explanation:

The possible combinations are 6 but one need to be careful when answering the question because of the clause "none or some"

The product rule says that if there are N ways of doing something and M ways of doing another thing, the number of ways of doing both things is equal to NM similarly if a third thing O is introduced then number of ways of combining the 3 items is NxMxO same for all numbers of combination

Since the order doesn't matter then the number of possible combination for 6 different topping is

1x2x3x4x5x6 or 6! = 720 however since the pizza can have none then should also be considered as a single combination so the total combination is 721