From a group of 7 people, you randomly select 4 of them.

What is the probability that they are the 4 oldest people in the group?


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.

From a group of 7 people, you randomly select 4 of them. What is the probability that they are the 4 oldest people in the group?

Discover how to calculate the probability of randomly selecting the 4 oldest people from a group of 7 using combinatorics and probability. Learn the step-by-step solution and explore related questions. This problem involves the combination formula and basic probability theory, making it suitable for students in Grades 10-12.

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