an ice cream shop offers 21 different flavors of ice cream and 6 different toppings. answer questions (a) through (d) using the appropriate counting technique (multiplication principle, arrangements with repetitions, permutations, or combinations). explain why you chose the particular technique.

a. how many different sundaes can you create using one of the ice cream flavors and one of the toppings? what counting technique will you use to make this calculation?

a. combinations because the selections come from a single group of items and the order of the arrangement does not matter.
b. the multiplication principle because there are m possible outcomes for one group and n outcomes for the other group.
c. permutations because the selections come from a single group of items and the order of the arrangement matters.
d. arrangements with repetitions because there are r selections from a group of n choices and you can repeat choices.

you can create different sundaes.
(type a whole number.)

Question

an ice cream shop offers 21 different flavors of ice cream and 6 different toppings. answer questions (a) through (d) using the appropriate counting technique (multiplication principle, arrangements with repetitions, permutations, or combinations). explain why you chose the particular technique.

a. how many different sundaes can you create using one of the ice cream flavors and one of the toppings? what counting technique will you use to make this calculation?

a. combinations because the selections come from a single group of items and the order of the arrangement does not matter.
b. the multiplication principle because there are m possible outcomes for one group and n outcomes for the other group.
c. permutations because the selections come from a single group of items and the order of the arrangement matters.
d. arrangements with repetitions because there are r selections from a group of n choices and you can repeat choices.

you can create   different sundaes.
(type a whole number.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fundamental Counting Principle" ], "new_concepts": [], "current_concepts": [ "Fundamental Counting Principle", "Combinatorics" ] } ## Identify the counting technique The problem asks for the number of sundaes made by choosing one flavor from a group of 21 flavors and one topping from a group of 6 toppings. Since we are making one selection from each of two distinct groups, we use the multiplication principle (also known as the fundamental counting principle). ## Calculate the number of sundaes Using the multiplication principle: $$ \text{Total sundaes} = 21 \times 6 = 126 $$ ## Question 1 (A) Combinations because the selections come from a single group of items and the order of the arrangement does not matter.

(B) The multiplication principle because there are M possible outcomes for one group and N outcomes for the other group.

(C) Permutations because the selections come from a single group of items and the order of the arrangement matters.

(D) Arrangements with repetitions because there are r selections from a group of n choices and you can repeat choices. ## Question 2 You can create 126 different sundaes. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Fundamental Counting Principle" ] }

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Explanation:

Identify the counting technique

Calculate the number of sundaes

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Question 1

Question 2