Answer :
Final answer:
To determine the number of combination possibilities with repetition for selecting flavor scoops, we use the formula C(n + r - 1, r). With repetition, the number of combinations increases compared to non-repetitive scenarios. An example of calculating sugar content shows 13.5 teaspoons of sugar equal the amount in a grande Frappuccino.
Explanation:
The question is about determining the number of different combinations with repetition when choosing scoops of flavors for an Iced sugar-free Annihilator. In this scenario, repetitions are allowed, meaning the same flavor can be chosen more than once for the scoops. To find the number of combinations possible with repetition, we use the formula for combinations with repetition: C(n + r - 1, r), where 'n' is the number of different flavors available, and 'r' is the number of scoops desired. For example, if 'n' is 5 (CC, M, S, DC, B), and you want to know the combinations for 3 scoops ('r'), you would calculate C(5 + 3 - 1, 3).
In contrast, if you were not allowed to repeat flavors, once you choose a flavor such as B (Banana), you can't choose it again for the remaining scoops, so the number of available choices decreases. In cases without repetition, the standard combinations formula C(n, r) is used, where after choosing flavor B (Banana), you have 4 flavors left for the second scoop, hence you would calculate C(4, 1) for the second scoop choice.
An example related to sugar content comparison, a grande Starbucks Frappuccino contains 54 grams of sugar. Since one teaspoon of sugar is equivalent to 4 grams of sugar, you would need 13.5 teaspoons of sugar to match the sugar content of a Frappuccino.
