Answer :
Final answer:
The student can order 30 different ice cream orders if they only consider one flavor per cone or cup. However, if they allow for two different flavors in a 2-scoop cone, the number of different orders increases to 120.
Explanation:
Your question relates to the mathematical concept of combination, which is used to determine how many possible ways you can arrange or choose items, regardless of their order. There are three types of cones or cups you can choose (1-scoop cone, 2-scoop cone, 1-scoop cup), and there are 10 different flavors. So, if you can only choose one type of cone and one flavor of ice cream to go in it, the total number of different ice cream orders you can make is 3 types of cones * 10 flavors = 30 different orders.
However, if you're considering a 2-scoop cone where the two scoops can be different flavors, the number of orders increases. In this case, you'll have 10 choices for the first scoop and 10 choices for the second scoop, giving 10 * 10 = 100 possible flavor combinations for the 2-scoop cone alone. Add the 1-scoop cone and 1-scoop cup options back in and you'll get 100 (for the 2-scoop cone) + 10 (for the 1-scoop cone) + 10 (for the 1-scoop cup) = 120 different orders.
Learn more about combination here:
https://brainly.com/question/37999460
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