# Choose President & 2-Person Committee from 8 People - 168 Ways

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In summary, the purpose of choosing a President and 2-person committee from 8 people in 168 ways is to understand and demonstrate the different combinations and permutations that can result from strategic decision making. There are 168 possible combinations that can result from this exercise, calculated using the formula nCr = n! / r!(n-r)! Several factors should be considered when making this decision, such as qualifications, skills, and teamwork. It is also possible for the same person to hold both the position of President and be a member of the 2-person committee, resulting in a smaller pool of candidates. The number of people to choose from directly affects the total number of combinations, with a higher number of people resulting in a higher number of possible
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## Homework Statement

In how many ways can a president and a 2-person committee be chosen from a group of 8 people (where the order in which we choose the 2 people doesn't matter)? (The president cannot be on the committee.)

## Homework Equations

nCr = n!/(r!*(n-r!))

## The Attempt at a Solution

8C1(for president) * 7C2(for committee)
=
8*21
=
168 ways

Did I do it right?

Correct.

Yes. There are also multiple ways to do this problem. You could have done ${}_8 C_3 \times 3 = 168$.

## What is the purpose of choosing a President and 2-person committee from 8 people in 168 ways?

The purpose of this exercise is to understand the various combinations and permutations that can result from selecting a President and 2-person committee from a pool of 8 people. It can also be used to demonstrate the importance of strategic decision making and the impact it can have on the overall outcome.

## How many possible combinations can result from choosing a President and 2-person committee from 8 people?

There are 168 possible combinations that can result from choosing a President and 2-person committee from 8 people. This is calculated by using the formula nCr = n! / r!(n-r)! where n is the total number of people (8) and r is the number of positions to be filled (3).

## What factors should be considered when choosing a President and 2-person committee from 8 people?

There are several factors that should be taken into consideration when choosing a President and 2-person committee from 8 people. These include the qualifications, skills, and experience of each individual, their ability to work together as a team, and their potential impact on the organization or group as a whole.

## Can the same person hold both the position of President and be a member of the 2-person committee?

Yes, it is possible for the same person to hold both the position of President and be a member of the 2-person committee. This would result in a smaller pool of candidates to choose from, as there would only be 7 people available for the remaining position on the committee.

## How does the number of people to choose from affect the total number of combinations?

The number of people to choose from directly affects the total number of combinations. As the number of people increases, the total number of possible combinations also increases. For example, if there were 10 people instead of 8, there would be 252 possible combinations instead of 168.

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