Combinatorics

One experiment results in n outcomes and and other in m there are mn possible outcomes in both the experiments together

r experiments that result in $n_1$ for the relative experiment, the possible outcomes are $$n_1\cdot n_2.......n_r$$

Permutations

Permutations are Ordered arrangements

If n objects are to be arranged (where placement matters) and there are n number of spaces, there are n! posible arrangements

n objects are to be arranged but $n_1,n_2...n_r$ are alike, then the number of arrangements will be $$\frac{n!}{n_1!n_2!.....n_r!}$$

Order is irrelevant. The number of combinations of a set of data is$$C^n_r=\frac{n!}{(n-r)!r!}$$ Where:

Total combinations = combinations with a particular object + combinations without that object $$C^n_r=C^{n-1}{r-1}+C^{n-1}{r}$$