My pizzeria offers
pizzas in 3 sizes (S/M/L)
7 different meat toppings
5 different vegetable toppings
4 different kinds of cheese.
How many different pizza orders are possible if we must pick a size, 1 meat, 2 different vegetables, and 1 kind of cheese?
300
The order of these items does not matter so I will use combinations
Size -- C(3,1) = 3
meats --C(7,1) = 7
veggies --C(5,2) = 10
cheese -- C(4,1) = 4
number of pizzas = 3x7x10x4 = 840
To calculate the number of different pizza orders, you need to multiply the number of choices for each component of the pizza.
First, you need to choose a size, which can be either small (S), medium (M), or large (L). Since there are 3 sizes to choose from, there are 3 options for this component.
Next, you need to choose 1 meat topping out of the 7 available options. There are 7 choices for this component.
Then, you need to choose 2 different vegetable toppings out of the 5 available options. To calculate the number of combinations, you can use the formula for choosing k items out of a set of n items, which is nCk = n! / (k!(n-k)!). In this case, you want to choose 2 vegetables out of the 5 available options, so the number of combinations is 5C2 = 5! / (2!(5-2)!) = (5 x 4) / (2 x 1) = 10.
Finally, you need to choose 1 kind of cheese out of the 4 available options. There are 4 choices for this component.
To find the total number of different pizza orders, you multiply the number of choices for each component: 3 (sizes) x 7 (meat toppings) x 10 (combinations of 2 vegetables) x 4 (cheese options) = 840.
Therefore, there are 840 different pizza orders possible if you must pick a size, 1 meat, 2 different vegetables, and 1 kind of cheese.