20+The+Fundamental+Counting+Principle


 * The Fundamental Counting Principle**

Everyone can count. That is a given. But it is how much you want to count which will determine when you will use certain formulas to make the job easier. Sometimes there are less outcomes, therefore making it easier to count down and list. Other times, it is easier, and more efficient to use a formula to count the number of outcomes/get your answer.


 * Fundamental Counting Principle Formula:**

If one event can occur in //m// ways and another event can occur in //n// ways, then the number of ways that both events can ocur is equal to **//m x n//.**

This priniple can be extended to three or more events. For instance, if three events can occur in //m//, //n//, and //k// ways, then the number of ways that all three can occur is **m x n x k.**


 * Fundamental Counting Principle Example Problems:**

1. Joey wants to flip a coin and roll a die. There are 2 ways that you can flip a coin and 6 ways that you can roll a die. Therefore, there are **2** x **6** = **12** ways that you can flip a coin **//and//** roll a die.

2. Joey wants to play the piano and also play the banjo. There are 88 notes on the piano and 5 notes on the banjo. Therefore, there are **88** x **5** = **440** ways that you can play a note on the piano **//and//** play the banjo.

3. Joey was playing cards and he wanted to draw 2 cards from a standard deck of 52 cards without replacing them. There are 52 ways to draw the first and 51 ways to draw the second. Therefore, there a are a total of **52** x **51** = **2652** ways to draw the two cards.


 * Fundamental Counting Principle Helpful Websites:**

1. http://people.richland.edu/james/lecture/m116/sequences/counting.html 2. http://www.algebra-class.com/fundamental-counting-principle.html 3. http://www.basic-mathematics.com/fundamental-counting-principle.html