Statistics : Combinations and Permutations
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Example Questions
Example Question #1 : Probability
There are four different colored marbles in a jar—red, blue, white, and black—calculate how many outcomes are possible if a person picks two of the marbles if the order in which the marbles are picked matters.
Cannot be determined
Outcomes are not always easily identified or calculated; however, mathematical operations associated with permutations and combinations can make these processes easier. Permutations provide the number of outcomes when the order of events matter. Permutations are calculated using the following formula:
In this formula, the variable, 
Let's use this information to solve the problem. We know that this is a permutation because the order of the marbles matters. We need to assign numbers to each of the variables we have for items or marbles and we have two slots or bins that they are to be ordered into; therefore, we know the following:
Now, we need to calculate the number of permutations present in this model; however, we need to understand how to perform calculations involving factorials. Factorials are denoted with an exclamation point (!). For example, let's observe the following operation:
This denotes that for every non-negative integer, 
Let's use this information to solve our marble example.
Solve.
Simplify.
We know that there are twelve possible permutations.
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