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.

Explanation:

Identify the counting scenario

Using the Fundamental Counting Principle knowledge point

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Match the appropriate technique

Using the Fundamental Counting Principle knowledge point

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Answer:

• 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. (Correct answer)
• 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.