pt 2 Flashcards
Combinations
These answer the question, How many ways are r things arranged in n potential seats if only the contents of r matter not their arrangement? it is the total number of ways to arrange n things divided by the number of arrangements where ONLY order changes. It is given by n!/((n-r)! r!). This can also be written as nPr/r! or the number of unique ways to arrange r items from n divided by how many ways there are to arrange the same r items in r positions, removing uniqueness.
What does (n-r)! and (n-r)!*r! mean?
(n-r)! represents the number of places where nothing within the set of n items will exist. (n-r)!*r! is a denominator term in combinations. The first part eliminates the parts of n that are irrelevant and r! is the number of unique ways to arrange r things. Hence dividing by r! means that you are counting for only the contents of the items in r positions and NOT the unique placement.
What is the meaning of r!
This is the number of ways you could arrange r items within r # of spots uniquely.
Permutation
nPr is the number of unique ways to arrange r items from n set of items. It is equal to n!/(n-r)! which is basically saying in option 1 we have n possiblilities in 2 we have n-1… until we reach n-r