Hotmath
Combinations
Combinationsare a method of selectingsubsets(in which order does not matter) from a largerset.
For example, you might be asked how many possible groups of three can be made from a set of five individuals. If you list out all possible groups, regardless of order, you will realize that groupsare all the same group of three people.
The trick here is to do thepermutationproblem first, then divide out by the number of different orders for each group. In this case:
But this includes all the “duplicates” of each group of. Each group ofcan be arranged in ways, so we need to divide thepermutations by! (or为了得到的数量groups where order does not matter.
In general, if you want to find the number of groups ofindividuals that can be selected from a set of, first find然后除以.
Moving theto the denominator, we get:
Example:
A quality inspector samplescell phones out of a batch of. How many different possible samples could she select?