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The problem states:

- There are 5 freshmen, 2 sophomores, 4 juniors, and 3 seniors forming a committee.
- A group of 4 people is needed to work on the social media account.
- We need to calculate the probability that the group contains **at most 2 juniors**.

Let's break this problem down:

### Step 1: Total number of ways to select 4 people
There are a total of \( 5 + 2 + 4 + 3 = 14 \) people available. The number of ways to choose a group of 4 people from 14 is given by the combination formula \( \binom{n}{k} = \frac{n!}{k!(n-k)!} \), where \( n \) is the total number of people and \( k \) is the number of people to choose.

So, the total number of ways to select 4 people from 14 is:
\[
\binom{14}{4}
\]

### Step 2: Number of ways to select 4 people with at most 2 juniors
We can have:
- 0 juniors in the group
- 1 junior in the group
- 2 juniors in the group

For each of these cases, we will compute the number of ways to choose the juniors and the remaining people from the non-juniors (freshmen, sophomores, and seniors).

- **Case 1: 0 juniors**  
  Choose 0 juniors from 4 juniors and 4 people from the 10 non-juniors:
  \[
  \binom{4}{0} \times \binom{10}{4}
  \]

- **Case 2: 1 junior**  
  Choose 1 junior from 4 juniors and 3 people from the 10 non-juniors:
  \[
  \binom{4}{1} \times \binom{10}{3}
  \]

- **Case 3: 2 juniors**  
  Choose 2 juniors from 4 juniors and 2 people from the 10 non-juniors:
  \[
  \binom{4}{2} \times \binom{10}{2}
  \]

### Step 3: Probability
The probability is the ratio of the favorable outcomes (total number of ways to choose a group with at most 2 juniors) to the total number of outcomes (total number of ways to choose 4 people from 14).

Let me calculate this now.The total number of ways to select 4 people from 14 is 1001. 

The number of favorable outcomes, where the group has at most 2 juniors, is 960.

Thus, the probability that the group contains at most 2 juniors is approximately **0.959** (rounded to four decimal places).

Would you like further details or have any other questions?

Here are 5 related questions for practice:
1. What is the probability that there are exactly 3 juniors in the group?
2. What is the probability of selecting a group with at least 1 sophomore?
3. How many ways can we form a group with exactly 1 freshman and 1 senior?
4. What is the probability that no freshmen are selected in the group of 4?
5. If the group is expanded to 5 people, how does the probability of having at most 2 juniors change?

**Tip:** When dealing with combinations, always consider breaking down complex problems into cases to make calculations manageable.

5 freshmen, 2 sophomores, 4 juniors, and 3 seniors form a committee. The committee needs a group of 4 people to work on its social media account. What is the probability that this social media group of 4 people has at most 2 juniors in it? Enter your answer in decimal form rounded to four decimal places if rounding is necessary.

Calculate the probability of forming a group of 4 people from a committee of freshmen, sophomores, juniors, and seniors, where the group contains at most 2 juniors. Learn the use of combinatorics and probability theory in this scenario.

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