Question

a. The number of ways to select a president, a vice president, and a secretary is

Ask by Newton Turnbull. in the United States
Jan 22,2025

Real Tutor Solution

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Answer

To find the number of ways to select a president, a vice president, and a secretary, you need to know the total number of people available. If there are \( n \) people, the number of ways is \( n \times (n - 1) \times (n - 2) \).

Solution

It appears that some information is missing from your question. To determine the number of ways to select a president, a vice president, and a secretary, I need to know the total number of people available for these positions. **For example:** - **If you have _n_ people to choose from:** The number of ways to select distinct individuals for the three positions is given by permutations since the order matters (each position is unique). \[ \text{Number of ways} = n \times (n - 1) \times (n - 2) \] This is often denoted as \( P(n, 3) \). - **If the positions can be held by the same person (allowing repetition):** The number of ways would be: \[ \text{Number of ways} = n \times n \times n = n^3 \] However, typically for positions like president, vice president, and secretary, each position is held by a different person, so the first scenario is usually applicable. **Please provide the total number of candidates available**, and I can give you a more specific answer!

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Mind Expander

Imagine you have a club with a group of enthusiastic members, and you want to choose a president, a vice president, and a secretary. For the president, you have the freedom to pick anyone, let’s say there are 10 members; that gives you 10 glowing choices! Once you have chosen a president, only 9 remain for the vice president’s spot, and then just 8 for the secretary. So, you multiply those choices together: 10 * 9 * 8 = 720 ways to select this trio! Now, thinking about real-world applications, this selection process mirrors situations in businesses or schools where leadership roles must be filled. Understanding permutations helps teams efficiently allocate roles or plan events where specific positions carry distinct responsibilities. It’s like assembling your dream team, ensuring you have the best people in place to drive the mission forward. How cool is that?

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