Permutations ...

Sonicwall

continued ...

At the end of this class answer the question:Why did we start by looking at this picture?

(a) How many numbers of 5 different digits each can be formed from the digits 0, 1, 2, 3, 4, 5, 6?

(c) How many of these numbers are divisable by 5?

(b) How many of these numbers are even?

verify this result

not zero

How many phone numbers can be made under the following conditions:(First digit cannot be 0 or 1 because you'll get the operator or long distance.) • The first two digits are 3 followed by 6 • The third digit is even • The fourth digit is greater than 5 • The fifth and seventh digits are odd • The sixth digit is 2

8 • 7 • 6 = 3361st 2nd 3rd

Solution as a PermutationSolution by the Fundamental Principle of Counting

Example: There are 8 horses in a race. In how many ways can three of them finish first, second and third?

A.K.A the "Pick" formula.

n is the number of objects to pick fromr is the number of objects to be arranged is read as "n pick r" means: Given a set of n objects, how many ordered arrangements can be made using only r of them at a time?

Formula:

Permutation: An ordered arrangement of objects without repetition.

How many ways can the batting order of a 9-member softball team be listed?

A 120-room hotel has reservations from 6 guests for 6 different rooms. In how many ways can the rooms be assigned?

How many different "words" can you make from the letters in the word BOOK?

# of I's = 4 # of S's = 4 # of P's = 2 ∴

# of O's = 2 ∴

Example: How many different "words" can be made form the letters in the word: (a) BOOK (b) MISSISSIPPI

The number of ways to arrange n objects that containsets of non-distinguishable objects is given by:

Permutations of Non-Distinguishable Objects

How many different "words" can you make from the letters in the word STATISTICS?