To find the probability that the 4 randomly selected people are the 4 oldest people in the group of 7, we can approach this problem using combinations.

Step 1: Total number of ways to select 4 people from 7

The total number of ways to select 4 people from a group of 7 is given by the combination formula:

$\binom{7}{4} = \frac{7!}{4!(7-4)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$

Step 2: Number of favorable outcomes

There is only 1 favorable outcome where the 4 selected people are exactly the 4 oldest people.

Step 3: Probability

The probability is the ratio of favorable outcomes to the total outcomes. So the probability $P$ is:

$P = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{1}{35}$

Thus, the probability that the 4 randomly selected people are the 4 oldest is:

$P = \frac{1}{35}$

Do you have any questions or would you like more details?

Here are 5 related questions you might find interesting:

1. How many different ways can you select 3 people from 7?
2. What is the probability of selecting exactly 3 of the 4 oldest people?
3. What is the probability of selecting the 3 youngest people from the group?
4. If we increase the group to 10 people, what is the probability of selecting the 4 oldest?
5. How many ways can you arrange 4 people out of a group of 7?

Tip: When dealing with probabilities involving random selections, using combinations helps calculate how many different ways an event can occur.