Question

A pizza parlor offers 8 different specialty pizzas. If the Almeida family wants to order 2 specialty pizzas from the menu, which method could be used to calculate the number of possibilities?

8 factorial divided by 2 factorial
8 factorial divided by 6 factorial
8 factorial divided by the quantity 6 factorial times 2 factorial end quantity
12!

Answer 1

To find the number of ways the Almeida family can order 2 specialty pizzas out of 8, we use the combinations formula C(8, 2) = 8! / (2!6!). This formula calculates the number of different combinations possible without regard to the order of selection.

Step-by-step explanation:

To calculate the number of different possibilities for the Almeida family to order 2 specialty pizzas from a menu of 8 different pizzas, we must determine the number of combinations possible. We use the combinations formula which is given by C(n, k) = n! / (k!(n-k)!) where n is the total number of items to choose from, in this case, 8 pizzas, and k is the number of items to be chosen, which is 2 pizzas.

In this scenario, the correct calculation would be 8 factorial divided by the quantity 6 factorial times 2 factorial, which simplifies to C(8, 2) = 8! / (2!*(8-2)!) = 8! / (2!*6!). This calculation accounts for the fact that the order in which the Almeida family selects the two specialty pizzas does not matter.