Question

At Beast Island Pizza, every pizza comes with cheese and tomato sauce. Beast Island Pizza offers four toppings: Pepperoni, sausage, mushrooms, and onions. Customers can add any number of toppings to a pizza, but Beast Island Pizza does not let customers double up on toppings or add extra cheese to a pizza.
Due to popular demand, Beast Island Pizza has agreed to make half-and-half pizzas. Each topping can now be added to either half of the pizza or the whole pizza. In how many different ways could a customer order a pizza?

Answer 1

Using the Fundamental Counting Theorem, there are 60 different ways to order the pizza.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

For this problem, considering the sauce, the topping and the pizza format, the parameters are found as follows:

• For the sauce, there are 2 options, either cheese or tomato, hence $n_1 = 2$.

• For the topping, there are 4 options, but the options may be combined, for example, Pepperoni and Sausage, hence $n_2 = 2^4 - 1= 15$. The subtraction by 1 is because the option of no topping is found in the third parameter.

• The topping can be added to either all the pizza or only half the pizza, hence $n_3 = 2$.

Thus the number of ways for the customer to order a pizza is given by:

N = 2 x 15 x 2 = 60.

More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866

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