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EECS 203 Exam 2 Cheat Sheet by

Combos, Permutations, Sequences, Pigeonhole Principle

Permut­ations, no repetition

permut­ation formula, ORDER MATTERS (i.e. ways to sort 5 of 10 students in a line)

Permut­ations, repetition

very easy, just use product rule as shown

Combin­ations, no repetition

combin­ation formula, ORDER does NOT matter (i.e committee of 3 out of 5 students)

Combin­ations, repetition

Bars and stars! Order does not matter, ways to select bills/­fruit and place in a container

C/P Quick table

quick reference

Binomial Theorem

binomial theorem... coeffi­cient is a Combin­ation.

Pascal's identity

binomial coeffi­cients, a recursive definition

Finite probab­ility

event over sample space. event is a subset of sample space

Compliment of probab­ility event

technique to calculate some probab­ilities

Probab­ility of union of 2 events

useful for proving things

Condit­ional Probab­ility

probab­ility of E given F E|F

Definition of indepe­ndent event

use for proofs

Pigeonhole Principle

if k is a positive integer and k+1 or more objects are placed into boxes, at least 1 box has 2+ objects

Bernoulli trials probab­ility of success


Baye's theorem

calculate probab­ility of i.e diseas­es/­dia­gnosis, probab­ility of spam...


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