Elementary counting techniques

* Probability And Statistics
* 2. Elementary Counting Techniques
* Imagine you are going to organize a meeting with your classmates and for lunch you must decide between different drinks andthree kinds of food. In how many ways can you choose what they consume?

In many daily life cases it is common to have to choose between one form or another there will be no great difficulty ifthere are a few forms among which to choose
The difficulties will appear when you carry out the counting of the different ways to choose where there are a greater number of elements
In many cases ofthe daily life as well as in different areas of knowledge is involved counting
Counting techniques are useful tool for enumerating the elements of a situation that is difficult to quantify

*Fundamental Principle of counting

* Suppose you must choose between apple or orange soda, and between burger tacos or hot dogs
* Visualizing it:

*
If an event can occur in n1 formsand another can occur in other n2 forms, then the number of ways in which both events can occur is that order is n1 • n2 different ways. This principle can be extended to three or more events

*This leads onto the fundamental counting principle..

* Example 1

* Find the number of outcomes that can be presented from tossing two coins into the air
* Each coin has two possibleoutcomes therefore
* (2)(2) = 4 different results

* Example 2

* Suppose you have to count the different car plates that can be made with three digits, the first digit cannot be zero.How many different car plates can you count?

* Solution

* One of the plates can be 123 another 124 and so on. There are 10 digits and the plate will have three: in the first position canbe any of the numbers 1 to 9 in the second position can vary from 0 to 9 and in third position from 0 to 9 , therefore :

(9)(10)(10)=900

* Example...