
Define combinatorial analysis (or combinatorics)
Combinatorics is a branch of mathematics that studies countable discrete structures. It includes studying counting, ordering and other problems.

The basic principle of counting
If event A has m possible outcomes, and event B has n possible outcomes, then there are m*n possible outcomes of the two experiments together.

Number of permutations of n objects
n*(n1)*(n2)*...*3*2*1 = n!

Number of permutations of n objects, of which n_{1} are alike, n_{2} are alike, ... n_{r} are alike.

The number of distinct subsets of size k that can be selected from a set of n objects (order of objects is irrelevant)
, a.k.a. the binomial coefficient.

The number of distinct ordered subsets of size k that can be selected from a set of n objects (order of objects is relevant)

Pascal's Rule (a combinatorial identity about binomial coefficients)
, for 1 ≤ r ≤ n

The binomial theorem
 Binomial theorem describes the algebraic expansion of powers of a binomial.

The number of subsets of a set of n elements
2^{n }^{ }(this includes the null subset)

The number of possible partitions of a set of n objects into r distinct groups (order irrelevant)
, a.k.a. the multinomial coefficient

The multinomial theorem

 (the sum is over all nonnegative integers n_{1}, n_{2}, ..., n_{r} such that n_{1}+n_{2}+...+n_{r }= n)

The number of distinct positive integervalued vectors satisfying

The number of distinct nonnegative integervalued vectors satisfying

Type I error
 A false positive
 The null hypothesis is rejected when it is actually true.
 "I falsely think that the Alternative hypothesis is true."

Type II error
 A false negative
 The null hypothesis is accepted when it is actually false.
 "I falsely think that the Alternative hypothesis is false."

