Hey Paze.

Basically combinations don't distinguish between the ordering.

As an example lets say we have a sequence of observations with either an A or a B. A few examples of length five include AABBA and ABABA.

Now in combinations, we don't care about the order of the sequence but only that the number of elements of a given type is the same.

In a permutation we distinguish ABABA from AABBA but in combinations we only care that we have three A's and two B's.

This is why in combinations we have a lower amount and this is compensated by a factorial.

nPr = n!/(n-r)! and nCr = n!/[r!*(n-r)!].

With the combinations, we are looking for the number of times we get a sequence with a certain number of events. A sequence that has two events is called a Binomial distribution and the distribution with n events is a Multinomial.

The above happens when every element of the sequence has the same probability as any other element.

So thats the main thing: in combinations we don't care about order but only that we have a sequence with a specific count of events (so in binomial, we have so many A's and so many B's but the order or arrangement is not important).