Tom and Jerry are hoping to be selected from their class of 25 as president and vice-president of the Social Committee (they just want the positions, but don't care which of the two is the president). If the three-person committee (president, vice-president, and secretary) is selected at random, what is the probability that Tom and Jerry would be president and vice president?

Round your answer to six decimal places.

Let's solve this problem step by step.

### Step 1: Total number of ways to select a president, vice-president, and secretary
The committee consists of 3 people: president, vice-president, and secretary. These positions are distinct, so the order in which people are selected matters.

- There are 25 students to choose from for the president.
- After selecting the president, there are 24 remaining students to choose from for the vice-president.
- After selecting both the president and vice-president, there are 23 remaining students to choose from for the secretary.

Thus, the total number of possible ways to form the committee is:
\[
\text{Total selections} = 25 \times 24 \times 23 = 13800
\]

### Step 2: Favorable outcomes for Tom and Jerry as president and vice-president
Tom and Jerry are hoping to be selected as the president and vice-president. Since they don't care who holds which position, we consider both cases:

1. Tom is the president and Jerry is the vice-president.
2. Jerry is the president and Tom is the vice-president.

There are 2 favorable outcomes for these cases, and for each case, there are 23 remaining students to choose from for the secretary. Thus, the number of favorable outcomes is:
\[
\text{Favorable outcomes} = 2 \times 23 = 46
\]

### Step 3: Probability
The probability is the ratio of favorable outcomes to the total number of outcomes:
\[
\text{Probability} = \frac{46}{13800} \approx 0.003333
\]

### Final Answer:
The probability that Tom and Jerry will be selected as president and vice-president is approximately \( \boxed{0.003333} \).

Would you like more details, or have any further questions?

Here are five related questions:
1. What is the probability that Tom or Jerry is chosen as the secretary?
2. How does the probability change if there are 30 students in the class?
3. What if there are 2 vice-presidents instead of just one?
4. How many distinct committees can be formed if positions were not distinct?
5. What if Tom and Jerry cared about who held which position?

**Tip:** In probability problems, identifying whether order matters (permutations) or does not matter (combinations) is key to solving correctly.

Tom and Jerry are hoping to be selected from their class of 25 as president and vice-president of the Social Committee (they just want the positions, but don't care which of the two is the president). If the three-person committee (president, vice-president, and secretary) is selected at random, what is the probability that Tom and Jerry would be president and vice president?

Explore the probability problem of Tom and Jerry being selected as president and vice-president from a class of 25. Learn how to calculate total selections, favorable outcomes, and final probability using permutation concepts. Suitable for high school students in Grades 9-12.

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