Permutations and Combinations

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 (143)(2)

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 • 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

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

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

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

Permutations and Combinations