Final answer:
Cory and Shana can choose from 360 different kitchen designs for their new home by applying the fundamental counting principle to their 4 cabinetry, 3 countertop, 6 flooring, and 5 appliance choices.
Step-by-step explanation:
Cory and Shana's choices for cabinetry, countertop, flooring, and appliances for their new kitchen design can be calculated using the fundamental counting principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m x n ways of doing both. In this scenario, they have 4 cabinetry options, 3 countertop options, 6 flooring options, and 5 appliance options to choose from.
Thus, the total number of different kitchen designs possible can be calculated as:
- Number of cabinetry choices: 4
- Number of countertop choices: 3
- Number of flooring choices: 6
- Number of appliance choices: 5
Using multiplication for independent choices, we get:
Total kitchen designs = (Number of cabinetry choices) x (Number of countertop choices) x (Number of flooring choices) x (Number of appliance choices)
Total kitchen designs = 4 x 3 x 6 x 5
Total kitchen designs = 360
Therefore, there are 360 different kitchen designs possible for Cory and Shana to choose from for their custom-built home.