Question

10. How many three-topping pizzas can be ordered from the list of toppings below? Did you calculate the number of permutations or the number of combinations to get your answer?
Why did you make this choice?
Pizza Toppings
sausage
pepperoni
meatball
onions
olives
spinach
pineapple
ham
green peppers
mushrooms
bacon
hot peppers

Answer 1

Step-by-step explanation:

Total numbers of pizza toppings = 12

Number of three topping pizzas can be ordered are:

$P^{n}_{k}=\frac{n!}{(n-k)!}$

where = n = number of elements

k = number of elements choosen

n= 12 , k = 3

$\frac{12!}{(12-3)!} =\frac{12\times 11\times 10\times 9!}{9!}= 1,320$

We calculated the number of permutations. We made this choice because in permutation order of element matters but in combination its not.