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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:
(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.

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