An ice cream shop offers 18 different flavors of ice cream and 12 different topp

Question

An ice cream shop offers 18 different flavors of ice cream and 12 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. Arrangements with repetitions because there are r selections from a group of n choices and you can repeat choices. O B. The multiplication principle because there are M possible outcomes for one group and N outcomes for the other group. ° C. Combinations because the selections come from a single group of items and the order of the arrangement does not matter O D. Pemutations because the selections come from a single group of items and the order of the arrangement matters. You can create ? different sundaes. (Type a whole number.) b. How many different triple cones can you create from the 18 flavors if the same flavor may be used more than once? Assume that you specify which flavor goes on the bottom, middle and top. What counting technique will you use to make this calculation? A. Arrangements with repetitions because there are r selections from a group of n choices and you can repeat choices. O B. Combinations because the selections come from a single group of items and the order of the arrangement does not matter. ° C. The multiplication principle because there are M possible outcomes for one group and outcomes for the other group. D. Permutations because the selections come from a single group of items and the order of the arrangement matters. You can create different triple cones. Type a whole number.) c. Using the 18 flavors, how many different triple cones can you create with 3 dilfferent flavors if you specify which flavor goes on the bottom, middle and top? What counting technique will ycu use to make this calculation? o A. The multiplication principle because there are M possible outcomes for one group and N outcomes for the other group. B. Permutations because the selections come from a single group of items and the order of the arrangement matters. ° C. Arrangements with repetitions because there are r selections from a group of n choices and you can repeat choices. O D. Combinations because the selections come from a single group of items and the order of the arrangement does not matter

Explanation / Answer

(a)

Option B is correct

total sundaes = 18 x 12 = 216

(b)

Option A is correct

total sundaes = 18 x 18 x 18 = 5832

(c)

Option B

repetition of flavors not allowed

total sundaes = P (18,3) = 18 x 17 x 16 = 4896

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