When it comes to forming committees, it’s important to know how many different options are available. In this case, we have a group of 10 people, and we need to know how many different committees of 7 people can be formed. Let’s take a closer look at the math behind this question.
Understanding Combinations
To solve this problem, we need to use a mathematical concept known as combinations. Combinations are a way to count the number of possible ways to choose a set of items from a larger set, where the order of the items does not matter.
In our case, we want to choose a committee of 7 people from a group of 10 people. Since the order of the people on the committee does not matter, we can use combinations to calculate the number of different committees that can be formed.
The formula for calculating combinations is:
nCr = n! / r!(n-r)!
where n is the total number of items in the set, and r is the number of items we want to choose.
Solving the Problem
Using the combinations formula, we can calculate the number of different committees of 7 people that can be formed from a group of 10 people:
10C7 = 10! / 7!(10-7)!
Simplifying this expression, we get:
10C7 = 120
Therefore, there are 120 different committees of 7 people that can be formed from a group of 10 people.
Conclusion
In conclusion, we can see that the answer to the question “how many different committees of 7 people can be formed from a group of 10 people?” is 120. This calculation was done using the combinations formula, which is a useful tool for counting the number of possible ways to choose a set of items from a larger set.
As you can see, having a solid understanding of math can be incredibly useful in a variety of situations. Whether you’re forming committees or calculating budgets, knowing how to use math effectively can help you make informed decisions and achieve your goals. So the next time you’re faced with a problem like this one, remember to use the combinations formula to find the solution.
