Combinations-different way to form groups of people

In summary, combinations are a way of forming groups of people by selecting a certain number of individuals from a larger pool without regard to their order. They differ from permutations in that they do not consider the order of the objects. The formula for calculating combinations is nCr = n! / (r! * (n-r)!). Combinations can be used in various real-life scenarios, but they have limitations, such as only being applicable when order does not matter and assuming all objects are unique.
  • #1
Stat_Newbie
1
0
Hello everyone,

I am new to this forum. Need help with this problem

How many ways you can select 3-person groups from a group of 8 students?

My solution:
----------------
Number of ways to make one group of 3 persons = 8C3
How do I proceed from here?

Thank you.
 
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  • #2
Apply the formula nCr = [itex]\frac{n!}{(n-r)! r!}[/itex]
or just simply use a calculator
 

FAQ: Combinations-different way to form groups of people

1. What are combinations in terms of forming groups of people?

Combinations refer to the different ways in which a group of people can be formed by selecting a certain number of individuals from a larger pool. It is a way of arranging or selecting objects without regard to their order.

2. How are combinations different from permutations?

Combinations and permutations are both ways of arranging or selecting objects, but the main difference is that combinations do not take into account the order of the objects, while permutations do. In other words, in combinations, the order of the objects does not matter, but in permutations, it does.

3. What is the formula for calculating combinations?

The formula for calculating combinations is nCr = n! / (r! * (n-r)!), where n represents the total number of objects and r represents the number of objects being selected.

4. Can combinations be used in real-life scenarios?

Yes, combinations are commonly used in real-life scenarios, such as in sports team selection, jury selection, and lottery number combinations. It is also used in genetics to determine the possible genotypes of offspring from two parents.

5. Are there any limitations to using combinations?

One limitation of using combinations is that it can only be applied to situations where the order of the objects does not matter. If order is important, permutations should be used instead. Additionally, the formula for calculating combinations assumes that all objects are unique, so it may not be applicable in situations where there are duplicate objects.

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