Combinations are just an application of the counting principle?

[skrying]

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? :!)

 

[mathman]

Pardon my ignorance. What is "the counting principle"?

 

[skrying]

The counting principle

The counting principle is dealing with the occurrence of more than one event, thus being able to quickly determine how many possible outcomes exist.
Kind of like sequences, if that makes more sense.

 

[robert Ihnot]

Counting principal for multiplication is: If something can be done in A ways and something else can be done in B ways, then the entire event can be done in AB ways.
For addition it means that in disjoint sets A and B, if we have K choices in A and L choices in B, then we have K+L choices in A union B.

Combinations and permutations then seem to be just that, applications of the counting principal. Possibly, skrying is aware that the combinations of N things taken K at a time is:

\frac{N!}{K!(N-K)!} And for permutations: \frac{N!}{(N-K)!}

 

[skrying]

Thank you Robert

Thank you Robert, that explanation and the examples were really helpful. You explained it so it actually "makes sense" to me. Much appreciated!