Question

Show complete work on your worksheet! You many use the !, nCr and nPr functions on your calculator to CHECK your calculations, but you must show the formulas with appropriate values substituted in first. Martino's Pizza offers a special pizza with 4 toppings. There are 11 toppings to choose from. Guido decides to order a different 4-topping pizza each day.

Answer 1

The number of varieties of pizza that can be made using 4 toppings from 11 toppings is 330.

Step-by-step explanation:

The number of varieties of pizza that can be made using 4 toppings can be calculated using the concept of combinations. To find the number of combinations, we can use the formula for nCr, which represents the number of ways to choose r objects from a set of n objects. In this case, n = 11 (number of toppings) and r = 4 (number of toppings to choose from).

The formula for nCr is nCr = n! / (r!(n-r)!), where n! represents n factorial. Factorial is the product of all positive integers from 1 to n. For example, 4! = 4 x 3 x 2 x 1 = 24.

Substituting the values into the formula, we get: 11C4 = 11! / (4!(11-4)!) = 11! / (4!7!) = (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 330.

Therefore, there are 330 different varieties of pizza that can be made using 4 toppings from a selection of 11 toppings.