15.3 Permutations and Combinations OBJ:  To solve problems involving permutations and combinations.

Slides:

Advertisements

Similar presentations

Permutations and Combinations

Advertisements

Permutations and Combinations

Warm Up Evaluate  4  3  2   6  5  4  3  2  1

Section 9.1b… Combinations. What are they??? With permutations, we take n objects, r at a time, and different orderings of these objects are considered.

Statistics Review. Box-and-Whisker Plots The Parts of a Box and Whisker Plot Name the parts of a Box-and-Whisker Plot MedianUpper Quartile Lower.

How many possible outcomes can you make with the accessories?

Permutations & Combinations

Lecture 07 Prof. Dr. M. Junaid Mughal

Permutations and Combinations AII Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish.

Expected value a weighted average of all possible values where the weights are the probabilities of each outcome :

Warm Up Evaluate  4  3  2   6  5  4  3  2  Permutations and Combinations.

College Algebra Fifth Edition

P ERMUTATIONS AND C OMBINATIONS Homework: Permutation and Combinations WS.

15.3 Permutations and Combinations. Warm-up Suppose a club with 5 members wishes to choose a president, vice president and treasurer. In how many ways.

Introductory Statistics Lesson 3.4 A Objective: SSBAT determine the number of permutations. Standards: M11.E

Counting Techniques 0.4.

Permutations and Combinations. Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish permutations.

Methods of Counting Outcomes BUSA 2100, Section 4.1.

Chapter 10 – Data Analysis and Probability

© The McGraw-Hill Companies, Inc., Chapter 4 Counting Techniques.

Part 2 – Factorial and other Counting Rules

The local Family Restaurant has a daily breakfast special in which the customer may choose one item from each of the following groups: Breakfast Sandwich.

Prob/Stats Definition A permutation is an ordered arrangement of objects. (For example, consider the permutations of the letters A, B, C and D.)

Chapter PERMUTATIONS AND COMBINATIONS. Objectives Solve problems involving the Fundamental Counting Principle. Solve problems involving permutations.

Objective: You should be able to solve problems involving permutations and combinations.

Permutations and Combinations

Permutations and Combinations

PERMUTATIONS AND COMBINATIONS BOTH PERMUTATIONS AND COMBINATIONS USE A COUNTING METHOD CALLED FACTORIAL.

Permutations and Combinations. Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish permutations.

Warm Up Evaluate  4  3  2   6  5  4  3  2 

Lesson 0.4 (Counting Techniques)

37. Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

Permutations and Combinations PSSA Unit. Permutations A permutation of the letters abc is all of their possible arrangements: abc acb bac bca cab cba.

Permutations and Combinations

Permutations and Combinations AII Objectives:  apply fundamental counting principle  compute permutations  compute combinations  distinguish.

Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

13 Lesson 1 Let Me Count the Ways Fundamental Counting Principle, Permutations & Combinations CP Probability and Statistics FA 2014 S-ID.1S-CP.3S-CP.5.

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Happy Pi Day! Find x. 15 If you still have x

Chapter 0.4 Counting Techniques.

Discrete Math Section 15.3 Solve problems using permutations and combinations Read page Combinations and permutations.

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

In this lesson, you will learn to use the Fundamental Counting Principle.

Warm Up Permutations and Combinations Evaluate  4  3  2  1

Permutations and Combinations

Permutations and Combinations

Lesson 11-1 Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Objectives Solve problems involving the Fundamental Counting Principle. Solve problems involving permutations and combinations.

10.4 Permutations and Combinations

Permutations and Combinations

How many possible outcomes can you make with the accessories?

Bellwork Practice Packet 10.3 B side #3.

Objectives Solve problems involving the Fundamental Counting Principle. Solve problems involving permutations and combinations.

Probability Warm Up page 12- write the question you have 10 mins to complete it. See coaching on page 85.

Permutations and Combinations

Standard DA-5.2 Objective: Apply permutations and combinations to find the number of possibilities of an outcome.

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Lecture 7: Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Presentation transcript:

15.3 Permutations and Combinations OBJ:  To solve problems involving permutations and combinations

Permutation (Order Important) Arrangement Picture EX:  A club with 12 members wants to choose a president, vice-president, and treasurer. The order of choices is important: The order A, B, and C for president, vice-president, and treasurer, respectively, is different from the order B, A, and C for the 3 positions. The number of ways of filling the three offices is: = 1320 Each slate of officers is a permutation of 3 people from a set of 12, denoted as 12 P 3.

Combination (Order not impt.) Committee If the club only wanted to select a committee of 3 out of its 12 members, order is not important. Each of the following selections: ABC, ACB, BAC, BCA, CAB, CBA are the same. To determine the number of different committees of three that can be chosen you would need to divide the previous total by = 6 = 220 Each committee is a combination of 3 people from a set of 12, denoted as 12 C 3.

Permutation (order important) Example 12 P 3 = ! (12 – 3) ! = 1320 Formula n P r = n (n-1)(n-2)... (n-r+1)(n-r)! (n – r)! = n!__ (n - r )!

Combination (order not important) Example 12 C 3 = = (12–3)! (12 – 3)! 3! = 220 Formula n C r = n (n-1)(n-2)... (n-r+1)(n-r)! (n-r)! r = n!__ ( n - r )! r!

EX:  A company advertises two job openings, one for a copywriter and one for an artist. If 10 people who are qualified for either position apply, in how many ways can the openings be filled? Fundamental Counting Principle 10 9 = 90 Permutation Formula 10 P 2 = 10! (10 – 2)! ! 8! 10 9 = 90

EX:  A company advertises two job openings for computer programmers, both with the same salary and job description. In how many ways can the openings be filled if 10 people apply. Fundamental Counting Principle = 90 2 = 45 Combination Formula 10 C 2 10! (10 – 2)! 2! ! 8! 2! = 90 2 = 45

EX:  For a raffle, 845 tickets are sold. a)In how many ways can four $50 gift certificates be awarded 845 C 4 845! (845-4)! 4! ,000,000,000 b) In how many ways can a $100, a $50, a $20m and a $10 gift certificate be awarded? 845 P 4 845! (845-4)! ,000,000,000

EX:  At the Red Lion Diner, an omelet can be ordered plain or with any or all of the following fillings: cheese, onions, and peppers. How many different kinds of omelets are possible? a) 3 C 3 3! __ (3 – 3)! 3! 1 b) 3 C 2 3! __ (3 – 2)! 2! 3 c) 3 C 1 3!_ _ (3 – 1)! 1! 3 d) 3 C 0 3!__ (3 – 0)! 0! 1 3 C C C C = 8