*A football team with 32 squad and 20 have arrived at an airport to board flights to a tournament. There are only 16 flights available due to severe weather and each flight can accommodate as many as 3 people. However, a draft player has already given up his boarding benefit by ground transport because he has no intention. How many complete teams can be guaranteed to appear in the tournament if the flights are randomly assigned to the players?*

Options:

A) 0

B) 1

C) 2

D) n-1

Let's go through the problem step by step.

### Problem Restatement:
- A football team with **32 squad members** has **20 players** ready to board flights.
- **16 flights** are available, with each flight accommodating **up to 3 people**.
- One draft player has opted out of the flight.
- We need to determine how many complete teams can be guaranteed to appear in the tournament if flights are randomly assigned to the players.

### Analyzing the Problem:
1. **Initial Number of Players:**
   - There are 20 players ready to board flights.

2. **Draft Player Opt-Out:**
   - Since one draft player opted out, we have \( 20 - 1 = 19 \) players left to board flights.

3. **Flight Capacity:**
   - Each of the 16 flights can accommodate 3 players.
   - Total capacity = \( 16 \times 3 = 48 \) players.

   However, since we only have 19 players, not all flights will be used to their full capacity.

### Key Question: How many complete teams can be guaranteed?

- **Complete Team Definition:** If we consider a "complete team" as a group of 3 players, then the maximum number of complete teams that can be formed with 19 players is calculated by dividing 19 by 3.

\[
\text{Number of complete teams} = \left\lfloor \frac{19}{3} \right\rfloor = 6 \text{ complete teams}, \text{ with 1 player left over}.
\]

### Interpretation of Answer Choices:
- The answer choices are somewhat abstract, so we have to consider them carefully.

### Conclusion:
- With 19 players, **6 complete teams** (groups of 3 players) can be formed.
- Since the choices are not explicitly numbered based on 6, but rather abstract options, none of the options explicitly mentions "6" as a direct answer. However, the answer **D) n-1** typically refers to a situation where one less than a complete set of something is achieved. 

In this context, **n-1** could be interpreted as the number of teams minus one, which makes **6 complete teams** the plausible answer since it might be interpreting \(n-1\) as a generalization for achieving a team or a similar number close to full.

**Correct interpretation of the given options is tricky**, but based on the specific scenario:

- **Answer:** Since \(n-1\) could be taken as the number of groups close to completion, **D) n-1** would be the best fit.

Would you like to explore more about how abstract answer choices work, or do you have any questions?

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Here are 5 related questions:

1. How would the number of complete teams change if there were 21 players instead of 20?
2. If only 15 flights were available, how would that affect the number of complete teams?
3. What is the minimum number of flights required to ensure that at least 5 complete teams can be formed?
4. How many possible ways are there to assign 19 players to 16 flights?
5. If each flight could only take 2 players instead of 3, what would be the impact on the number of complete teams?

**Tip:** When analyzing problems with abstract or indirect answer choices, try to interpret the options relative to the specific problem setup. Understanding how "n" or similar variables are defined in context is crucial.

Learn how to determine the number of complete football teams that can attend a tournament based on flight assignments. This problem involves combinatorics and division concepts. Suitable for high school students studying probability and combinatorial mathematics.

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