Respuesta :
Answer:
You could order 16 different kinds of pizza.
Step-by-step explanation:
You have those following toppings:
-Pepperoni
-Sausage
-Mushrooms
-Anchovies
The order is not important. For example, if you choose Sausage and Mushrooms toppings, it is the same as Mushrooms and Sausage. So we have a combination problem.
Combination formula:
A formula for the number of possible combinations of r objects from a set of n objects is:
[tex]C_{(n,r)} = \frac{n!}{r!(n-r!}[/tex]
How many different kinds of pizza could you order?
The total T is given by
[tex]T = T_{0} + T_{1} + T_{2} + T_{3} + T_{4}[/tex]
[tex]T_{0}[/tex] is the number of pizzas in which there are no toppings. So [tex]T_{0} = 1[/tex]
[tex]T_{1}[/tex] is the number of pizzas in which there are one topping [tex]T_{1}[/tex] is a combination of 1 topping from a set of 4 toppings. So:
[tex]T_{1} = \frac{4!}{1!(4-1)!} = 4[/tex]
[tex]T_{2}[/tex] is the number of pizzas in which there are two toppings [tex]T_{2}[/tex] is a combination of 2 toppings from a set of 4 toppings. So:
[tex]T_{2} = \frac{4!}{2!(4-2)!} = 6[/tex]
[tex]T_{3}[/tex] is the number of pizzas in which there are three toppings [tex]T_{3}[/tex] is a combination of 3 toppings from a set of 4 toppings. So:
[tex]T_{3} = \frac{4!}{3!(4-3)!} = 4[/tex]
[tex]T_{0}[/tex] is the number of pizzas in which there are four toppings. So [tex]T_{4} = 1[/tex]
Replacing it in T
[tex]T = T_{0} + T_{1} + T_{2} + T_{3} + T_{4} = 1 + 4 + 6 + 4 + 1 = 16[/tex]
You could order 16 different kinds of pizza.
