GRE数学考点：set、排列、组合.docx

GRE数学考点：set、排列、组合

Set
A set is a collection of objects or things. Each object in a set a member
or element of that set.Size of a set is the number of members in the set.
Example:
The set of even numbers between 2 and 10 is of size 5:{2,4,6,8,10}.
The set of primes between 2 and 10 is of size 4:{2,3,5,7}.
Remember:
Each member of set A belongs to A or is in the set A.
A set can not have repeating member:{1,3,1,2}is not a set.
Rearranging the order of the members does not change the set:{1,2,3}is same
as{3,2,1}.
Combinations
Number of ways we can select n objects from a group of m distinct objects
is m!/(n!*(m-n)!).
Example:
Number of possible ways to pick 4 oscar nominations from a list of 50
movies is 50!/(4!*(50-4)!)=50!/(4!*46!)=50*49*48*47/24=230300.
Remember:
This does not apply if there are identical objects.
Permutation of Objects
The number of ways n distinct objects can be ordered is n!.
Example:
Number of ways 6 people can from a queue is 6!.
Number of ways 5 different cars can be parked in 5 parking spaces is
5!.
Remember:
This does not apply if there are identical objects or ordering does not
matter.