Contents
 • one choice • many choices: permutations • many choices: combinations • many choices: combinations • independent events • dependent events • permutations without repettitions • permutations with identical elements • combinations • coditional probabilities • and or events • two outcomes • total probability theorem • Bayes rule • union sets and probability • fundamental counting principle

 Other exercices

 Combinatorics - Probability
Fundamental Counting Principle

Fundamental Counting Principle

Let's consider the 2 following sets of books:
Physics = {Physics1, Physics2, Physics3}, and
Math = {Math1, Math2}

We just need a pair of books: one of Physics and one of Math. How many ways do we have to do that?

The 6 ways that we have are:
(Physics1,Math1)
(Physics1,Math2)
(Physics2,Math1)
(Physics2, Math2)
(Physics3, Math1)
(Physics3, Math2)

The total is 6 ways.

We have 3 ways to choose a Physics book, and 2 ways to choose a Math book. Therefore 3 x 2 = 6 ways to choose a pair of books.

Gegerally, if there are m ways to perform an event, and n ways for independent another, then there are m x n ways of perform both. This is the fundamental counting principle.

Independent event Ai : mi ways
The total number of ways is: ? mi.

 Today: : ____________

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