There are 30 players who are divided into 6 even teams. What are the odds that two specific people are in the same team?

To determine the probability that two specific players are on the same team, let's follow these steps:

1. **Total Players and Teams**: There are 30 players divided into 6 teams, so each team will have \( \frac{30}{6} = 5 \) players.

2. **Choosing Teams for Specific Players**: To find the probability that two specific players are on the same team, we consider the following:
   - If two specific players are on the same team, they are part of the same group of 5.
   - The first player can be in any of the 6 teams.
   - Once the first player is placed, the second player must be in the same team for them to be together.

3. **Calculating the Probability**:
   - **Total ways** to assign the second player: The second player can be placed in any of the 6 teams, so there are 6 possibilities.
   - **Favorable outcomes**: There is only 1 favorable outcome where the second player joins the same team as the first player.

So, the probability that the two specific players are in the same team is:
\[
\text{Probability} = \frac{1}{6}
\]

This probability is 1/6 or approximately 0.1667.

Would you like to dive deeper into this calculation, or do you have any other questions?

Here are some related questions to consider:

1. What is the probability that two specific players are in different teams?
2. How would the probability change if there were 7 teams instead of 6?
3. What if three specific players are involved? What's the probability that they are all in the same team?
4. How many different ways can the 30 players be divided into 6 teams?
5. If you randomly pick a player, what is the probability that they are on a specific team?
6. How does the probability change if the number of teams is reduced to 5?
7. Can we calculate the odds that two players are not on the same team?
8. What is the probability that exactly two of three specific players are on the same team?

**Tip**: When dealing with probability problems, it is often useful to think about the total number of possible outcomes and the number of favorable outcomes to calculate the probability.

Explore the probability that two specific players are on the same team in a group of 30 players divided into 6 teams. Learn how to calculate this probability step-by-step, considering combinatorial methods and basic probability principles. Suitable for high school students and those interested in probability theory.

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