Step-by-Step Solution:
To determine the missing combination, we start by listing all the given sets of gelato flavors and then identifying any missing combinations from the list provided.
1. List the given flavors:
- Hazelnut (H)
- Chocolate (C)
- Tiramisu (T)
- Pistachio (P)
- Strawberry (S)
2. Identify all possible 3-flavor combinations from these flavors:
To find all combinations of three flavors from five, we use the `n choose k` formula which calculates combinations. Here [tex]\( n = 5 \)[/tex] (the total flavors), and [tex]\( k = 3 \)[/tex]:
[tex]\[
\text{Number of combinations} = \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5!}{3! \cdot 2!} = 10
\][/tex]
Here are the combinations:
- (H, C, T)
- (H, C, P)
- (H, C, S)
- (H, T, P)
- (H, T, S)
- (H, P, S)
- (C, T, P)
- (C, T, S)
- (C, P, S)
- (T, P, S)
3. List the combinations given in the problem and identify which ones are missing:
Given combinations:
- (H, C, T)
- (H, C, S)
- (H, T, S)
- (C, T, P)
- (C, P, S)
- (H, C, P)
- (H, P, S)
- (T, P, S)
4. Find the missing combinations:
By comparing the full list of combinations to the provided list, we can identify the missing ones.
Missing:
- (H, T, P)
- (C, T, S)
Both choices A and B are in the required combinations. To check the options:
Options Provided in the Question:
A. S-T-H : This matches with (S, T, H) or (H, T, S)
B. C-T-S: This matches with (C, T, S)
C. H-T-P: This matches with (H, T, P)
D. P-T-S: This is not missing, as it is given.
All combinations check out, except for D because (P, T, S) is given.
Therefore, the missing combinations and correct choices are H-T-P (option C) and C-T-S (option B). The answer to the missing combination is:
Answer:
C. H-T-P
