13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent...

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13-1 Permutations and Combinations Pre Calc A

Transcript of 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent...

Page 1: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

13-1 Permutations and Combinations

Pre Calc A

Page 2: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Vocabulary

Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination

Page 3: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex 17:

Determine whether the events are independent or dependent.

Tossing 3 coins one at a time Choosing a president, vice president, and treasurer for a club Selecting a math, history, and science for next year The order in which runners finish 1st, 2nd, and 3rd in a race

Page 4: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex :

Mr. Douty is buying a suit, either one made of wool or one made of polyester. He has narrowed down the choices of colors to gray, blue, black, or tan and the matching tie to a floral, stripe, or solid. How many different selections of his suit and tie are possible?

Page 5: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex last one:

How many seven digit phone numbers begin with 28?

How many seven digit phone numbers begin with 28 if no digits can be repeated?

Page 6: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex 17:

How many different ways can 5 different textbooks be placed on a shelf?

Page 7: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex :

A high school honor club is composed of 7 students.

How many different ways can all the members stand in a straight line for a picture?

How many ways can they select a president and vice president ?

Page 8: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex :

A TV network has 15 movies they can show for the holidays. They have spots to air 3 of these movies. How many groups of three can be selected?

Page 9: 13-1 Permutations and Combinations Pre Calc A. Vocabulary Factorial Independent Events Dependent Events Basic Counting Principle Permutation Combination.

Ex last one: There are 10 names on the ballot for senior class

officers. Four will be selected to form a committee.

How many different committees of 4 can be formed?

In how many ways can a committee of 4 be formed if each student has a different responsibility?

If ther5e are 6 girls and 4 boys on the ballot, how many committees of 3 girls and 1 boy be formed?


Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER.

“Best” permutation for each model type determined by ranking RMSE, variance ratio, bias, and R 2 (Table 5). Arizona favored less complex variable permutations.

“Best” permutation for each model type determined by ranking RMSE, variance ratio, bias, and R 2 (Table 5). Arizona favored less complex variable permutations.

CHAPTER Permutations, Combinations, and the Binomial … 11.pdf... · 11 Permutations, Combinations, and the Binomial Theorem Key Terms fundamental counting principle factorial permutation

CHAPTER Permutations, Combinations, and the Binomial … 11.pdf... · 11 Permutations, Combinations, and the Binomial Theorem Key Terms fundamental counting principle factorial permutation

Elements of Combinatorics 1. Permutations (Weak Definition) A permutation is usually understood to be a sequence containing each element from a finite.

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ariste Galois and Solvable Permutation Groupsjlipman/553/Cox-Galois.pdf · For Galois, permutations are bijections {1,...,m}−→{roots} ⇐call these arrangements while substitutions

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0.5 – Permutations & Combinations. Permutation – all possible arrangements of objects in which the order of the objects is taken in to consideration.

0.5 – Permutations & Combinations. Permutation – all possible arrangements of objects in which the order of the objects is taken in to consideration.

Inversions on Permutations Avoiding Consecutive PatternsInversions on Permutations Avoiding Consecutive Patterns Naiomi Cameron* 1 Kendra Killpatrick2 12th International Permutation

Inversions on Permutations Avoiding Consecutive PatternsInversions on Permutations Avoiding Consecutive Patterns Naiomi Cameron* 1 Kendra Killpatrick2 12th International Permutation

Permutations and Combinations. Objectives Calculate a permutation. Calculate a combination. Determine whether you should use a combination or permutation.

Permutations and Combinations. Objectives Calculate a permutation. Calculate a combination. Determine whether you should use a combination or permutation.

Section 12.5 - Combinations & Permutations€¦ · Section 12.5 Combinations & Permutations PreCalculus May 18, 2015 Independent Events - Two events, A and B, are independent if the

Section 12.5 - Combinations & Permutations€¦ · Section 12.5 Combinations & Permutations PreCalculus May 18, 2015 Independent Events - Two events, A and B, are independent if the

9.1 Day 2-3 Notes PERMUTATIONS - Ms. Orloff · 9.1 Day 2-3 Notes PERMUTATIONS Permutation Counting Formula Sometimes, we have more objects than we have “spots/positons” to fill.

9.1 Day 2-3 Notes PERMUTATIONS - Ms. Orloff · 9.1 Day 2-3 Notes PERMUTATIONS Permutation Counting Formula Sometimes, we have more objects than we have “spots/positons” to fill.

5.Permutations and Combinations - Sakshi · 2014-10-30 · PERMUTATIONS AND COMBINATIONS Permutations are arrangements of things taken some or all at a time. In a permutation, order

5.Permutations and Combinations - Sakshi · 2014-10-30 · PERMUTATIONS AND COMBINATIONS Permutations are arrangements of things taken some or all at a time. In a permutation, order

12.4 – Permutations & Combinations. Permutation – all possible arrangements of objects in which the order of the objects is taken in to consideration.

12.4 – Permutations & Combinations. Permutation – all possible arrangements of objects in which the order of the objects is taken in to consideration.

Geometric generation of permutation sequenceshomepage.divms.uiowa.edu/~roseman/mathviz09D.pdf · 2009-03-26 · The mathematical objects we chose are permutations. Construct families

Geometric generation of permutation sequenceshomepage.divms.uiowa.edu/~roseman/mathviz09D.pdf · 2009-03-26 · The mathematical objects we chose are permutations. Construct families

Permutation and Dihedral Groups - mathcourses.nfshost.com · Overview Starting De nitions Factorizations of Permutations Cycle Structure of Permutations Orders of Permutations Parity

Permutation and Dihedral Groups - mathcourses.nfshost.com · Overview Starting De nitions Factorizations of Permutations Cycle Structure of Permutations Orders of Permutations Parity

3.4B-Permutations Permutation: ORDERED arrangement of objects. # of different permutations (ORDERS) of n distinct objects is n! n! = n(n-1)(n-2)(n-3)…3·2·1.

3.4B-Permutations Permutation: ORDERED arrangement of objects. # of different permutations (ORDERS) of n distinct objects is n! n! = n(n-1)(n-2)(n-3)…3·2·1.

Permutation Groups - Colorado State Universityhulpke/talks/CR/CR2.pdf · 2015. 4. 8. · permutation groups. Some Fundamental Tasks Groups of permutations of degree up to a few 106,

Permutation Groups - Colorado State Universityhulpke/talks/CR/CR2.pdf · 2015. 4. 8. · permutation groups. Some Fundamental Tasks Groups of permutations of degree up to a few 106,

Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of

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2.4 Permutations and Combinations - Gustavus …homepages.gac.edu/~rpark/mcs115/9780538495059-ch2.4.pdf2.4 Permutations and Combinations O bjectives • Develop and apply the Permutation

2.4 Permutations and Combinations - Gustavus …homepages.gac.edu/~rpark/mcs115/9780538495059-ch2.4.pdf2.4 Permutations and Combinations O bjectives • Develop and apply the Permutation

PERMUTATIONS AND COMBINATIONS - Prashanth Ellinancertbooks.prashanthellina.com/class_11.Mathematics.Mathematics/Ch... · PERMUTATIONS AND COMBINATIONS 139 Definition 1 A permutation

PERMUTATIONS AND COMBINATIONS - Prashanth Ellinancertbooks.prashanthellina.com/class_11.Mathematics.Mathematics/Ch... · PERMUTATIONS AND COMBINATIONS 139 Definition 1 A permutation

11.1 Permutation and Combination · Probability, Permutations, & Combinations Lesson 11.1 Objectives Define probability Use the counting principle Know the difference between combinations

11.1 Permutation and Combination · Probability, Permutations, & Combinations Lesson 11.1 Objectives Define probability Use the counting principle Know the difference between combinations