Tree diagrams

Many problems in Probability Theory require that we count the number of ways that a particular event can occur or the number of outcomes in the sample space. For this purpose, we need to use counting techniques. One of these techniques is the tree diagram.

For example: Mr. Arnold has in his closet 3 shirts, 2 pants and 2 pair of shoes. How many different ways can he dress every morning?

           Mr. Arnold’s Closet
 

List all of Mr. Arnold’s outfits:

There are 12 different outfits.
 
 
But there are situations in which counting is not too easy. For example if we have to count the different ways to sit 10 people in 10 chairs. For these situations we need Combinatorics. This is the branch of Mathematics that studies the different ways to group or order the elements of a set, that is:
–Variations
–Combinations
–Permutations 

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