Correct : b

Explanation:
1. Identify the Type of Problem:
• There are n = 4 distinct flavors available.
• We need to choose r = 3 scoops.
• Since we can choose the same flavor multiple times, repetition is allowed.
• Since the order of the scoops is inconsequential, this is a combinations problem with repetition (also known as the "Stars and Bars" or "Multichoose" problem).

2. Apply the Formula:
The number of ways to choose r items from a set of n distinct items with repetition allowed is given by the formula:
    ^{n + r - 1}C_r

3. Substitute the Values:
• n = 4 (flavors)
• r = 3 (scoops)
    Number of ways = ^{4 + 3 - 1}C₃ = ⁶C₃

4. Calculate the Combination:
    ⁶C₃ = (6 × 5 × 4) / (3 × 2 × 1) = 120 / 6 = 20

5. Conclusion: There are exactly 20 different ways to purchase the 3 scoops of ice-cream.