Permutations and Combinations
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Transcript of Permutations and Combinations
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