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The question asks for the probability that when selecting 5 people randomly from a group of 7, all 5 selected people are the oldest in the group.

This is a probability problem involving combinations. Let's break it down:

### Step 1: Total possible selections
You are selecting 5 people from a group of 7. The total number of ways to choose 5 people from 7 is given by the combination formula:

\[
\text{Total combinations} = \binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7 \times 6}{2 \times 1} = 21
\]

### Step 2: Favorable outcomes
The favorable outcome is selecting exactly the 5 oldest people. Since there is only one way to choose the 5 oldest, the number of favorable outcomes is 1.

### Step 3: Probability calculation
The probability is the ratio of favorable outcomes to total possible outcomes:

\[
\text{Probability} = \frac{1}{21}
\]

Thus, the probability that the 5 people selected are the 5 oldest is \( \frac{1}{21} \).

Would you like further details or have any questions about this explanation?

Here are 5 related questions for further exploration:
1. How would the probability change if you were selecting 4 people instead of 5?
2. How is the combination formula derived?
3. What would happen to the probability if you had 10 people and selected 6 of them?
4. What if the selection process wasn't random but had some conditions (e.g., a minimum age requirement)?
5. How does this scenario change if order matters in the selection?

**Tip:** For combination problems, remember that order does not matter, which is why combinations (not permutations) are used.

From a group of 7 people, you randomly select 5 of them. What is the probability that they are the 5 oldest people in the group? Give your answer as a fraction.

Learn how to calculate the probability of selecting the 5 oldest people from a group of 7, using combinations. Understand key concepts in probability and combinatorics with this step-by-step explanation. Suitable for students in Grades 9-12.

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