User:Temperal/The Problem Solver's Resource5
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 5. |
Contents
[hide]Combinatorics
This section cover combinatorics, and some binomial/multinomial facts.
Permutations
The factorial of a number is or also as ,and is denoted by .
Also, .
The number of ways of arranging distinct objects in a straight line is . This is also known as a permutation, and can be notated
Combinations
The number of ways of choosing objects from a set of objects is , which is notated as either or . (The latter notation is also known as taking the binomial coefficient.
Binomials and Multinomials
- Binomial Theorem:
- Multinomial Coefficients: The number of ways of ordering objects when of them are of one type, of them are of a second type, ... and of them of another type is
- Multinomial Theorem: . The summation is taken over all sums so that .
Ball and Urn
The ball and urn argument states that, there are this many ways to place balls in urns: