From a group of 12 people, you randomly select 3 of them.

What is the probability that they are the 3 oldest people in the group?

Give your answer as a fraction

To solve this problem, let's break it down into a few steps.

1. **Total possible ways to select 3 people from 12**:  
   We can choose any 3 people from a group of 12. The number of ways to do this is given by the combination formula:
   \[
   \binom{12}{3} = \frac{12!}{3!(12 - 3)!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220
   \]

2. **Favorable outcomes (selecting the 3 oldest people)**:  
   There is only 1 way to select the 3 oldest people out of the 12, as they are already defined as a specific subset.

3. **Probability calculation**:  
   The probability of selecting the 3 oldest people is the ratio of favorable outcomes to the total possible outcomes:
   \[
   \frac{1}{220}
   \]

So, the probability that the 3 selected people are the 3 oldest in the group is:
\[
\frac{1}{220}
\]

Would you like more details or have any questions?

### Related Questions:
1. What is the probability of selecting 2 oldest people and one younger person in the group?
2. How does the probability change if we select 4 people instead of 3?
3. If we select people one by one without replacement, what’s the probability that the 3 oldest are chosen consecutively?
4. What’s the probability of selecting any 3 specific individuals from a group of 12?
5. How many ways can we select 4 people from the group of 12?

#### Tip:
Remember that for calculating probabilities with combinations, it's often helpful to first determine the total and favorable outcomes separately, then form a ratio.

From a group of 12 people, you randomly select 3 of them. What is the probability that they are the 3 oldest people in the group? Give your answer as a fraction.

Learn how to calculate the probability of randomly selecting the 3 oldest people from a group of 12. This solution includes a step-by-step breakdown of using combinations and probability principles. Perfect for high school students studying combinatorics and probability.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation