Question

Godfathers is offering a special. You can have a 3-topping pizza for $6. They have 7 different toppings to choose from. How many different pizzas are possible?

a) 21

b) 35

c) 42

d) 49

Answer 1

To find the number of different 3-topping pizza combinations possible from a choice of 7 toppings, we use the combination formula C(7, 3), which results in 35 different combinations. Therefore, the answer is 35.

Step-by-step explanation:

The student's question about the number of different pizza combinations that can be created with 3 toppings from a choice of 7 is a problem of combinatorics, which is a field of mathematics. To find the answer, we can use the combination formula which is used to determine the number of ways to choose a subset of items from a larger set where the order of selection does not matter. The combination formula is given by C(n, k) = n! / (k!(n - k)!), where 'n' is the total number of items to choose from, and 'k' is the number of items to choose.

In this case, we have 7 different toppings (n=7) and we want to choose 3 of them (k=3). Plugging these values into the combination formula gives us:

C(7, 3) = 7! / (3!(7 - 3)!) = 7! / (3!4!) = (7×6×5) / (3×2×1) = 35

Therefore, there are 35 different 3-topping pizzas possible using 7 different toppings. So, the correct answer is b) 35.