Give an example problem where you would use Permutation skills and formula to solve. Solve your example problem showing all your steps.
Example problem:
A pizza shop offers 5 different toppings for their pizzas (pepperoni, mushrooms, onions, green peppers, and olives). How many different pizzas can be made if you can choose 3 toppings for each pizza?
Solution:
To solve this problem, we can use the permutation formula:
nPr = n! / (n-r)!
Where n is the total number of items to choose from and r is the number of items to choose.
In this case, n = 5 (number of toppings) and r = 3 (number of toppings to choose for each pizza).
Plugging in the values, we get:
5P3 = 5! / (5-3)!
= 5! / 2!
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= 120 / 2
= 60
Therefore, there are 60 different pizzas that can be made by choosing 3 toppings from the 5 available toppings.