新gre数学考点介绍：set、排列、组合和AT least One

　　AT least One

　　If probability of event A happening is p and event B happening is q, then the probability that at least one of them happens is (p+q).

　　Example:

　　There are 20 quarters, 33 nickels, and 47 pennies in a jar. The probability that a randomly selected coin is a quarter= 20/(20+33+47)=20/100=0.2 and the coin is nickel = 33/100 =0.33.The probability it is either a quarter or a nickel = 0.2+0.33=0.53.

　　Remember:

　　The events needs to be mutually exclusive, that is if one happens the other cannot happen: a coin is either a quarter or nickel but not both.

　　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.