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Peter sells 5 flavors of gelato (Italian ice cream) at his stand. Today he is selling Hazelnut, Chocolate, Tiramisu, Pistachio, and Strawberry. Allen wants to try three different scoops in his cone. Below is a list of possible combinations. What's missing?

\begin{tabular}{ccccc}
\hline [tex]$H - C - T$[/tex] & [tex]$H - C - S$[/tex] & [tex]$H - T - S$[/tex] & [tex]$C - T - P$[/tex] & [tex]$C - P - S$[/tex] \\
[tex]$H - C - P$[/tex] & [tex]$?$[/tex] & [tex]$H - P - S$[/tex] & [tex]$?$[/tex] & [tex]$T - P - S$[/tex] \\
\hline
\end{tabular}

A. [tex]$S - T - H$[/tex]
B. [tex]$C - T - S$[/tex]
C. [tex]$H - T - P$[/tex]
D. [tex]$P - T - S$[/tex]

Sagot :

GinnyAnsweridn
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
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