Combinations
Combinations are a method of selecting subsets of a larger set in which order is not important.
For example, you might be asked how many possible groups of three can be made from a set of five individuals. Here, groups ABC, ACB, BCA, BAC, CAB, and CBA are all the same group of three people.
The trick here is to do the permutation problem, but to divide out by the number of different orders for each group. In this case:
In general, if you want to find the number of groups of m individuals that can be selected from a set of n, first find nPm and then divide by m!.
This formula can be written more simply using factorials.
Example:
A sample of four cell phones taken from a batch of 100 cell phones is to be inspected. How many different samples could be selected?
