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Define combinatorial analysis (or combinatorics)
Combinatorics is a branch of mathematics that studies countable discrete structures. It includes studying counting, ordering and other problems.
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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.
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Number of permutations of n objects
n*(n-1)*(n-2)*...*3*2*1 = n!
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Number of permutations of n objects, of which n1 are alike, n2 are alike, ... nr are alike.
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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.
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The number of distinct ordered subsets of size k that can be selected from a set of n objects (order of objects is relevant)
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Pascal's Rule (a combinatorial identity about binomial coefficients)
 , for 1 ≤ r ≤ n
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The binomial theorem
 - Binomial theorem describes the algebraic expansion of powers of a binomial.
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The number of subsets of a set of n elements
2n (this includes the null subset)
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The number of possible partitions of a set of n objects into r distinct groups (order irrelevant)
 , a.k.a. the multinomial coefficient
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The multinomial theorem
 - (the sum is over all non-negative integers n1, n2, ..., nr such that n1+n2+...+nr = n)
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The number of distinct positive integer-valued vectors  satisfying 
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The number of distinct non-negative integer-valued vectors  satisfying
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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."
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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."
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