Combinations & Counting: Is There a Proven Formula?

In summary, combinations are an application of the counting principle, with the specific formula being C(n,p) = (n!)/(p!)(n-p!) for n>p. It is also true that A, if completely contained in B and B completely contained in C, is also completely contained in C.
  • #1
skrying
9
0
Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an application of the counting principle, then would their be a specific formula that proves as such?
 
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  • #2
the combination formula is : C(n,p) = (n!)/(p!)(n-p!) with n>p

is that what you have meant? :S
 
  • #3
If A is completely contained in B, and B is completely contained in C, then A is completely contained in C.
 
  • #4
Reply to A I and Who..

Yes, that was what I was looking for. Thank you for your help!
 

What is combinations and counting?

Combinations and counting is a branch of mathematics that deals with determining the number of possible combinations of a set of objects or events.

What is the difference between combinations and permutations?

Combinations and permutations both involve counting the number of possible arrangements of a set of objects. However, combinations do not consider the order of the objects, while permutations do.

Is there a proven formula for calculating combinations?

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

How is combinations and counting used in real life?

Combinations and counting can be used in various fields, such as statistics, probability, and computer science. It is commonly used in data analysis, gambling, and cryptography.

What are some common misconceptions about combinations and counting?

One common misconception is that combinations and permutations are the same thing. Another is that the order of objects does not matter in combinations. Additionally, many people believe that there is a single formula that can be applied to all combinations problems, when in reality, different scenarios may require different approaches.

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