Permutations refer to the arrangement of objects in a specific order. The key characteristic of permutations is that order matters.
If you have a set of n distinct objects and you want to arrange r of them, the number of permutations is given by:
$$ P(n,r) = \frac{n!}{(n - r)!}
$$
Combinations refer to the selection of objects from a set where order does not matter.
If you have a set of n distinct objects and you want to choose r of them without regard to order, the number of combinations is given by:
$$ C(n,r)= \frac{n!}{r!(n - r)!} $$
$$ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A \&B)}{P(B)} $$
[video]
$$ Probability: P(data|parameters) \\ Likelihood: L(parameters|data) $$
Probability: What is the chance of this data happening, given a specific model or parameters?
Likelihood: Given the data I observed, how plausible is a particular parameter value for my model?