Question

1. erik gets to choose from five cake flavors, seven icing flavors, and three topping flavors. if he can only choose one of each flavor, how many cakes are possible? (10 points)

35
21
573
105

Explanation:

Step1: Apply the fundamental counting principle

The fundamental counting principle states that if there are \(m\) ways to do one thing, \(n\) ways to do a second thing, and \(p\) ways to do a third thing, then the total number of ways to do all three things together is \(m\times n\times p\). Here, \(m = 5\) (cake flavors), \(n=7\) (icing flavors), and \(p = 3\) (topping flavors).

Step2: Calculate the product

$$5\times7\times3=(5\times7)\times3=35\times3 = 105$$

Answer:

105