11.8 Combinations A combination of items occurs when

Slides:

Advertisements

Similar presentations

Counting Principles Probability.

Advertisements

Warm-Up Problem Can you predict which offers more choices for license plates? Choice A: a plate with three different letters of the alphabet in any order.

Thinking Mathematically Combinations. A combination of items occurs when: The item are selected from the same group. No item is used more than once. The.

Permutations & Combinations Section 2.4. Permutations When more than one item is selected (without replacement) from a single category and the order of.

6-7 Permutations & Combinations M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle.

COMBINATORICS Permutations and Combinations. Permutations The study of permutations involved order and arrangements A permutation of a set of n objects.

4. Counting 4.1 The Basic of Counting Basic Counting Principles Example 1 suppose that either a member of the faculty or a student in the department is.

How many different ways can you arrange the letters in “may”?

April 22, 2010Math 132: Foundations of Mathematics 11.2 Homework Solutions 8. 10! = 3,628, P 7 = 8,648, P 3 = 6, !/(2!2!) =

MATH104 Ch. 11: Probability Theory. Permutation Examples 1. If there are 4 people in the math club (Anne, Bob, Cindy, Dave), and we wish to elect a president.

Today in Algebra 2? Turn in graded worksheet Notes: Permutations and Combinations –NEED A GRAPHING CALCULATOR Homework.

Counting Methods – Part 2 Determine the number of ways of getting a sequence of events.

Counting Principles. What you will learn: Solve simple counting problems Use the Fundamental Counting Principle to solve counting problems Use permutations.

Aim: Combinations Course: Math Lit. Do Now: Aim: How do we determine the number of outcomes when order is not an issue? Ann, Barbara, Carol, and Dave.

Permutations and Combinations

Methods of Counting Outcomes BUSA 2100, Section 4.1.

Counting and Probability It’s the luck of the roll.

Counting Techniques. Multiplication Rule of Counting If a task consists of a sequence of choices in which there are p selections for the first choice,

Basic Probability Permutations and Combinations: -Combinations: -The number of different packages of data taken r at time from a data set containing n.

Pg. 606 Homework Pg. 631#1 – 3, 5 – 10, 13 – 19 odd #1135#12126 #1370#14220 #151365# #1756x 5 y 3 #1856x 3 y 5 #19240x 4 # x 6 #34expand to.

Sullivan Algebra and Trigonometry: Section 14.2 Objectives of this Section Solve Counting Problems Using the Multiplication Principle Solve Counting Problems.

Aim #10-7: How do we use the permutation formula? A permutation is an ordered arrangement of items that occurs when: No item is used more than once. The.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.9 Combinations.

Combinations and Permutations CHAPTER 4.4.  Permutations are used when arranging r out of n items in a specific order. n P r = PERMUTATIONS.

A horse race has the following horses running. How many different first, second and third place results are possible: Mushroom Pepper Sausage Tomato Onion.

Permutations, Combinations, and Counting Theory

How many four-digit odd numbers are there? Assume that the digit on the left cannot be a zero.

6.7 Permutations & Combinations. Factorial: 4! = 4*3*2*1 On calculator: math ==> PRB ==> 4 7! = 5040 Try 12!

Honors PreCalculus: Section 9.1 Basic Combinatorics.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.

MATH 2311 Section 2.1. Counting Techniques Combinatorics is the study of the number of ways a set of objects can be arranged, combined, or chosen; or.

Choosing items from a larger group, when the order does not matter. This is different than permutations in chapter 11.2 – items had to be in a certain.

MATH260 Ch. 5: Probability Theory part 4 Counting: Multiplication, Permutations, Combinations.

Introduction to probability (2) Combinations التوافيق Definition of combination: It is a way of selecting items from a collection, such that the order.

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

Example A standard deck of 52 cards has 13 kinds of cards, with four cards of each of kind, one in each of the four suits, hearts, diamonds, spades, and.

4-1 Chapter 4 Counting Techniques.

MATH 2311 Section 2.1.

11.3 Notes Combinations.

Counting Methods and Probability Theory

12.2 Permutations and Combinations

Probability using Permutations and Combinations

Unit 4 – Combinatorics and Probability Section 4

4-1 Chapter 4 Counting Techniques.

4-1 Chapter 4 Counting Techniques.

Section 12.9 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

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

Lesson 11-1 Permutations and Combinations

11.6 Conditional Probability

Permutations and Combinations

104- Ch. 11 part 1; 260- Ch. 5 pt. 2 master_prob_pc.pptx

How many possible outcomes can you make with the accessories?

MATH 2311 Section 2.1.

Counting Methods and Probability Theory

Counting Principle.

Counting Methods and Probability Theory

Permutations and Combinations

Counting Methods and Probability Theory

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

Day 2 - Combinations.

What is the difference between a permutation and combination?

Exercise How many different lunches can be made by choosing one of four sandwiches, one of three fruits, and one of two desserts? 24.

Permutations and Combinations

________________________________________________

MATH 2311 Section 2.1.

Presentation transcript:

11.8 Combinations A combination of items occurs when The items are selected from the same group. No item is used more than once. The order of items makes no difference. Note: Permutation problems involve situations in which order matters. Combination problems involve situations in which the order of items makes no difference.

Examples 1 – 2: Determine which involve permutations and which involve combinations. Example 1: Six students are running for student government president, vice-president and treasure. The student with the greatest number of votes becomes the president, the second highest vote-getter becomes vice-president, and the student who gets the third largest number of votes will be treasurer. How many different outcomes are possible? Example 2: Six people are on the board of supervisors for your neighborhood park. A three-person committee is needed to study the possibility of expanding the park. How many different committees could be formed from the six people?

Comparing Combinations and Permutations Given the letters: A,B,C,D: We can compare how many permutations and how many combinations are possible if we chose 3 letters at a time:

The number of possible combinations if r items are taken from n items is: Example 3: While visiting New York City, the Friedmans are interested in visiting 8 museums but have time to visit only 3. In how many ways can the Friedmans select 3 of the 8 museums to visit?

Example 4: Jan Funkhauser has 10 different cut flowers from which she will choose 6 to use in a floral arrangement. How many different ways can she do so? Example 5: How many three-person committees could be formed from 8 people?

Example 6: At the Royal Dynasty Chinese restaurant, dinner for eight people consists of 3 items from column A, 4 items from column B, and 3 items from column C. If columns A, B, and C have 5, 7, and 6 items, respectively, how many different dinner combinations are possible? Example 7: In December, 2009, the U.S Senate consisted of 60 Democrats and 40 Republicans. How many committees can be formed if each committee must have 3 Democrats and 2 Republicans?