using the fundamental counting principle with three or more groups of items
A pizza can be ordered with three choices of size (small, medium, or large), four choices of crust (thin,thick,crispy, or regular, and six choices of toppings (ground beef, sausage, pepperoni, bacon, mushroom, or onions). How many one-topping pizzas can be ordered?
A pizza can be ordered with three choices of size (small, medium, or large), four choices of crust (thin, thick, crispy, or regular), and six choices of toppings (ground beef, sausage, pepperoni, bacon, mushrooms, or onions). How many different one-topping pizzas can be ordered?
To calculate the number of one-topping pizzas that can be ordered using the fundamental counting principle, we need to multiply the number of choices for each category.
Number of choices for size = 3 (small, medium, or large)
Number of choices for crust = 4 (thin, thick, crispy, or regular)
Number of choices for toppings = 6 (ground beef, sausage, pepperoni, bacon, mushroom, or onions)
To count the number of one-topping pizzas, we need to select one topping from the six available choices. Therefore, we have 6 choices for the topping.
Applying the fundamental counting principle, we multiply the number of choices for each category:
Number of one-topping pizzas = Number of choices for size * Number of choices for crust * Number of choices for toppings
= 3 * 4 * 6
= 72
So, there are 72 different one-topping pizzas that can be ordered.
To find the number of one-topping pizzas that can be ordered using the fundamental counting principle, we need to multiply the number of choices available for each category together.
First, we have three choices of size: small, medium, or large.
Next, we have four choices of crust: thin, thick, crispy, or regular.
Finally, we have six choices of toppings: ground beef, sausage, pepperoni, bacon, mushroom, or onions.
To find the number of one-topping pizzas, we need to consider that each pizza has only one topping. So, we only need to select one topping from the available six choices.
Let's calculate the possibilities:
Number of choices for size = 3
Number of choices for crust = 4
Number of choices for toppings = 6
Using the fundamental counting principle, we multiply these numbers together to find the total number of one-topping pizzas that can be ordered:
Total number of one-topping pizzas = Number of choices for size × Number of choices for crust × Number of choices for toppings
Total number of one-topping pizzas = 3 × 4 × 6
Total number of one-topping pizzas = 72
Therefore, there are 72 different one-topping pizzas that can be ordered.
There are three choices of size, four choices of crust and six choices of toppings.
These choices are independent of each other, so by the principle of multiplication, the number of one-topping pizzas is:
N=3*4*6 = 72