From a group of 7 people, 2 are randomly selected. What is the probability the 2 oldest people in the group were selected? Give your answer as a reduced fraction.

To determine the probability that the 2 oldest people in a group of 7 are selected, we can follow these steps:

1. **Total number of ways to select 2 people from a group of 7**:
   This is a combination problem, where we need to calculate the number of ways to choose 2 people from 7. The formula for combinations is:
   \[
   \binom{n}{k} = \frac{n!}{k!(n-k)!}
   \]
   where \( n \) is the total number of people, and \( k \) is the number of people to be selected. For our problem:
   \[
   \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21
   \]
   So, there are 21 possible ways to choose 2 people from a group of 7.

2. **Number of ways to select the 2 oldest people**:
   There is only 1 way to select the 2 oldest people from the group because we are specifically selecting those two individuals.

3. **Probability**:
   The probability is the ratio of favorable outcomes to the total outcomes. The favorable outcome is selecting the 2 oldest people, which is 1, and the total number of possible selections is 21. Therefore, the probability is:
   \[
   \frac{1}{21}
   \]

Thus, the probability that the 2 oldest people are selected is \( \frac{1}{21} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the probability of selecting any specific pair of people from the group?
2. How does the probability change if there were 8 people instead of 7?
3. What is the probability of not selecting the 2 oldest people?
4. How many different pairs can be selected if 3 people are chosen instead of 2?
5. How would you calculate the probability if more than 2 people were selected at random?

**Tip**: When dealing with selection problems, combinations are used because the order in which people are selected doesn't matter.

Learn how to calculate the probability of selecting the 2 oldest people from a group of 7. This problem involves combinatorics and probability, using the combination formula to determine the number of ways to choose 2 individuals from the group. Suitable for students in Grades 9-12.

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