From a group of 6 people, 5 are randomly selected. What is the probability the 5 oldest people in the group were selected? *Give your answer as a reduced fraction.*

To find the probability that the 5 oldest people are selected from a group of 6 people when 5 people are randomly chosen, we can break down the problem as follows:

1. **Total number of ways to select 5 people from a group of 6**:  
   The total number of ways to select 5 people out of 6 is given by the combination formula:
   \[
   \binom{6}{5} = \frac{6!}{5!(6-5)!} = \frac{6!}{5!1!} = 6
   \]
   So, there are 6 possible groups of 5 people that can be selected from the group of 6.

2. **Favorable outcomes**:  
   There is exactly **1 favorable outcome**, which is selecting the 5 oldest people from the group. This is just one specific combination out of the 6 possible selections.

3. **Probability calculation**:  
   The probability is the ratio of favorable outcomes to total outcomes, which is:
   \[
   P(\text{5 oldest}) = \frac{1}{6}
   \]

Thus, the probability that the 5 oldest people are selected is \( \frac{1}{6} \).

Would you like further clarification on any of the steps?

Here are 5 related questions for further exploration:
1. What is the probability of selecting exactly 4 of the 5 oldest people from the group?
2. How does the probability change if we randomly select 4 people instead of 5?
3. What is the total number of ways to arrange 5 people out of 6?
4. How can the combination formula be applied to larger groups?
5. What if the selection is ordered? How does that affect the outcome?

**Tip**: When dealing with probabilities, always check whether the selection process considers order (permutations) or is independent of order (combinations).

From a group of 6 people, 5 are randomly selected. What is the probability the 5 oldest people in the group were selected? Give your answer as a reduced fraction.

Learn how to calculate the probability of randomly selecting the 5 oldest people from a group of 6. This problem involves the combination formula and basic probability concepts. Suitable for high school students, Grades 9-12.

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