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Math 1400 Cheat Sheet (DRAFT) by

Final exam ch 3-7,10

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Counting

 

Multip­lic­ation principle

If one event can occur in m ways and another event can occur in n ways, then the two events together can occur in
m×n ways
Length 3 (1,2,3­,4,5,6)
6x6x6
  

Factorials

n!=n⋅(­n−1­)⋅(­n−2­)⋯3⋅2⋅1
0! = 1
1! = 1

Permut­ations

Ways to arrange items where order matters.
P(n)=n!
Arrange A, B, C → 3! = 6 ways
P(n,r)­=(n­−r)!n!​
Choose president, VP, secretary from 8 people: P(8,3)= 8!/5! ​
repeats n!/n1!­n2!...nk!
BANANA → 6 letters, repeats: A=3, N=2 6!/3!2! ​

Combin­ations

C(n,r)=(n r​)=n!­/r!­(n−r)!

Binomial Theorem

(a+b)^n
(a+b)n=k=0∑n​(n k​)an−kb^k