How Many Different Committees Of 7 People Can Be Formed From A Group Of 10 People?

Introduction

When it comes to organizing groups of people, it can be difficult to figure out how many different combinations are available and how they can be used. A common question that arises is “How many different committees of 7 people can be formed from a group of 10 people?” This is an important question to consider when planning events, meetings, or any other gathering where you need to divide a large group into smaller ones. In this blog post, we will explore the different possibilities for committees of 7 people when given a larger group of 10. We’ll look at the math involved and discuss some examples to provide more insight into this topic. Let’s get started!

The mathematics of committees

There are a lot of different ways to mathematically answer this question, but we will focus on one method in particular.

Let’s say you have a group of 10 people. How many different committees of people can be formed from this group?

One way to think about this is to use the fact that there are 10 factorial (10!) possible permutations of this group of 10 people. This means that there are 10! different ways that you could arrange these 10 people into a committee.

However, not all of these permutations are going to be unique committees. For example, if you had a group of 5 men and 5 women, there would be 5!x5! possible permutations, but only 10!/(5!x5!) unique committees, since the order of the men and the women within the committee does not matter.

Thus, if we want to find the number of unique committees that can be formed from a group of N people, we need to divide the N factorial by the product of all of thefactors within N!. So for our example above with 10 people, we would have:

10!/ (1x2x3x4x5x6x7x8x9x10) = 10!/ (1 x 2^9) = 1814400/512 = 35280

The different ways to form committees

There are a few different ways to form committees from a group of people:

-The first way is to choose a random group of people. This is the most common method and is often used when forming ad hoc committees.
-The second way is to select people based on their expertise or knowledge in a certain subject. This method is often used when forming committees for specific tasks, such as a committee to plan an event.
-The third way is to select people based on their ability to work well together. This method is often used when forming committees that will be working closely together on a project.

Conclusion

To sum up, when determining how many different committees of 7 people can be formed from a group of 10 people, the answer is 120. This answer can be determined by using a combination formula to calculate the number of possible committees. With this knowledge, it becomes easier to understand why there are so many possibilities when forming a committee and it also gives us insight into just how complex yet fun combinations mathematics can be.