Presentation on theme: "Chris Morgan, MATH G160 January 27, 2012 Lecture 8"— Presentation transcript:
1 Chris Morgan, MATH G160 firstname.lastname@example.org January 27, 2012 Lecture 8 Chapter 4.1:PermutationsChris Morgan, MATH G160January 27, 2012Lecture 8
2 Permutations• We use permutations when we are interested in the number of possible ways to order something and ORDER IS IMPORTANT!• When order is not important, then it is a combinationn – total number of objects to choose fromr – number of times you choose an objectThus a permutation is an ordered arrangement of “r” objects from a group of “m” objects.
3 8 * 7 * 6 = 336 Permutation example Suppose I have 8 different colors of gumballs. How many different ways can I give 3 children a gumball?8 * * 6 = 336
4 Permutation example Does this look like we simply used the BCR? - BCR and Permutation are related.- Let’s find out why using the permutation formula:
5 With replacement? or Without replacement? Sampling Replacement The outcome of a permutation depends on two things. Do we sample:With replacement?orWithout replacement?
6 Permutations with Replacement These aren’t popular, but let’s see what one might look like:How many possible ways could I select from the letters PURDUE if I sample with replacement?_ _ _ _ _ _6*6*6*6*6*6 = 66= 46656
7 Permutations without Replacement How many different letter arrangements can be formed using the letters BOILERS?Theorem: Special Permutations Ruleis the number of ways to order n distinct objects_ _ _ _ _ _ _So, there are 7! = 5040 ways to arrange the letters BOILERS.
8 Theorem There are: different permutations of m objects of which m1, m2, … mk are alike respectively.
9 _ _ _ _ _ _ _ _ _ _ A little bit harder now How many different ways to reorder the letters in the word Statistics?_ _ _ _ _ _ _ _ _ _How many different ways to reorder the letters in the word Probability?
10 Example (XVIII)At an academic conference, 12 faculties are going to take a picturetogether. There are 3 professors, 5 associate professors and 4assistant professors. If we want people at the same level to staytogether, how many ways to line them up?
11 Example (CLII)My new bike lock has three dials numbered between 0 and 9.How many different ways can the code be set if:No restrictions at all?None of the numbers may be the same?No two consecutive numbers may be the same?The third number must be lower than the second?
12 Example (XLII)You are required to select a 6-character case-sensitive password foran online account. Each character could be upper-case orlower-case letter or a number from 0 to 9.No restrictions at all?The first character can not be a number?The last four characters must all be different?There must be at least one capital letter and at least one number?
13 Example (MD)I want to have four friends over (five including myself) and I want to make sure none of us bring the same type of liquor. The VBS next to me sells 17 types of liquor. What’s the probability no two people bring the same kind of liquor?