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Permutations and Combinations. Nov. 27, 2007 Lucas Anderson. Fundamental Counting Principle. If 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 . Permutations. Rearrangement of elements in a set.

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permutations and combinations

Permutations and Combinations

Nov. 27, 2007

Lucas Anderson

fundamental counting principle
Fundamental Counting Principle
  • If 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
permutations
Permutations
  • Rearrangement of elements in a set

(143)(2)

slide4

n!=1x2x3….xn is the number of permutations of a set of n elements

  • The number of permutations of k objects of a set of n elements is
question
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)60

B)10

C)20

D)120

slide6

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)60

B)10

C)20

D)120

combinations
Combinations
  • Number of ways of selecting k objects from a set of n
  • Unordered objects
  • Also called binomial coefficient
question1
Question
  • 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

slide9

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