Example Question #6 : Statistics
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, , refers to the number of things or items in the model and the variable, , refers to the number of ways that items can be ordered (i.e. the number of bins or slots present in the model).
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, , we can define its factorial by calculating the product of all of the integers less than or equal to .
Let's use this information to solve our marble example.
We know that there are twelve possible permutations.