Nov. 27, 2007 Lucas Anderson

Permutations and Combinations

Fundamental Counting PrincipleIf the number of events is n, and the

number of outcomes for each experiment is for , then the total number of outcomes for all events is

PermutationsRearrangement of elements in a set

(143)(2)

n!=1x2x3….xn is the number of

permutations of a set of n elementsThe number of permutations of k objects of

a set of n elements is

Question

There are three seats left in a theatre and five people left to be seated. In how many different ways can they be seated?A)60B)10C)20D)120

There are three seats left in a theatre and five people left to be seated. In how many different ways can they be seated?

A)60B)10C)20D)120

CombinationsNumber of ways of selecting k objects

from a set of n

Unordered objectsAlso called binomial coefficient

QuestionThere are 20 seniors and 15 juniors. 3

juniors and 2 seniors are picked to form a committee. In how many ways can this be done?A) 119,700

B)1,436,400 C)1,037,400 D) 86,450

There are 20 seniors and 15 juniors. 3 juniors and 2 seniors are picked to form a committee. In how many ways can this be done?A) 119,700

B)1,436,400 C)1,037,400

D) 86,450