Pre-Calculus Section 8.6A Counting Principles. 1. Eight pieces of paper are numbered 1 to 8 and placed in a box. One piece of paper is drawn from the.

Slides:

Advertisements

Similar presentations

Counting Principles, Permutations, and Combinations

Advertisements

Counting Principles Probability.

4/16/2015 MATH 224 – Discrete Mathematics Counting Basic counting techniques are important in many aspects of computer science. For example, consider the.

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.

Sequences, Series, and Probability

___ ___ ___ ___ ___ ___ ___ ___ ___

Combinations We should use permutation where order matters

Introduction to Combinatorics. Objectives Use the Fundamental Counting Principle to determine a number of outcomes. Calculate a factorial. Make a tree.

3/26/03 Tucker, Applied Combinatorics Section General Counting Methods for Arrangements and Selections Tucker, Applied Combinatorics, Sec. 5.1,

Probability Using Permutations and Combinations

REMEMBER: A number can be negative or positive as shown in the number line below: Negative Numbers (-) Positive Numbers (+)

Consecutive Numbers An Investigation.

Chapter The Basics of Counting 5.2 The Pigeonhole Principle

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

The Fundamental Counting Principle and Permutations

Counting. Product Rule Example Sum Rule Pigeonhole principle If there are more pigeons than pigeonholes, then there must be at least one pigeonhole.

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

1 Fundamental Counting Principle & Permutations. Outcome-the result of a single trial Sample Space- set of all possible outcomes in an experiment Event-

Probability and Counting Rules CHAPTER 4.5.  Find the probability of getting four aces when five cards are drawn from an ordinary deck of cards. FOUR.

Probability Counting Methods. Do Now: Find the probablity of: Rolling a 4 on a die Rolling a “hard eight” (2 - 4’s) on a pair of dice.

Lesson  The numerator and denominator of a theoretical probability are numbers of possibilities.  Sometimes those possibilities follow regular.

The Basics of Counting Section 6.1.

MAT 142 Lecture Video Series. Introduction to Combinatorics.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.8 The Counting Principle and Permutations.

Ch Counting Principles. Example 1  Eight pieces of paper are numbered from 1-8 and placed in a box. One piece of paper is drawn from the box, its.

CSNB143 – Discrete Structure

Discrete Structures Counting (Ch. 6)

Counting Principles Multiplication rule Permutations Combinations.

CLICK THE NUMBERS IN SEQUENCE

How Many is Too Many? A counting principle investigation.

Honors PreCalculus: Section 9.1 Basic Combinatorics.

 Counting  Fundamental Counting principle  Factorials  Permutations and combinations  Probability  Complementary events  Compound events  Independent.

8.6 Counting Principles. Listing Possibilities: Ex 1 Eight pieces of paper are numbered from 1 to 8 and placed in a box. One piece of paper is drawn from.

Learning to count to 10 in Spanish with your favorite TV Characters!

Section 1.3 Each arrangement (ordering) of n distinguishable objects is called a permutation, and the number of permutations of n distinguishable objects.

ONE TWO THREE FOUR FIVE SIX SEVEN EIGHT NINE TEN CLICK THE NUMBERS IN SEQUENCE.

Skip Counting Practice

Chance of winning Unit 6 Probability. Multiplication Property of Counting  If one event can occur in m ways and another event can occur in n ways, then.

Section Basic Counting Principles: The Product Rule The Product Rule: A procedure can be broken down into a sequence of two tasks. There are n 1.

CS 104: Discrete Mathematics

Mean Mean  = Sum of all the values The number of values Eg. Find the mean of the following values: 2, 5, 4, 7, 5, 7, 8, 4, 5, 6, 12, 2, 4, 5, 7, 5 Mean.

Box 1Box 2Box 3 Box 4Box 5Box 6 Box 7Box 8Box Counting Principle Tic Tac Toe Press F5. Take turns choosing boxes. The person who chose the box has.

ICS 253: Discrete Structures I Counting and Applications King Fahd University of Petroleum & Minerals Information & Computer Science Department.

SECTION 5.4 COUNTING. Objectives 1. Count the number of ways a sequence of operations can be performed 2. Count the number of permutations 3. Count the.

Section The Product Rule  Example: How many different license plates can be made if each plate contains a sequence of three uppercase English letters.

© 2010 Pearson Prentice Hall. All rights reserved. 1 §11.5, Probability with the Fundamental Counting Principle, Permutations, and Combinations.

WHAT IS BINARY? Binary is a number system that only uses two digits: 1 and 0. Any information that processed by a computer it is put into sequence of.

Counting Principles Ex. Eight pieces of paper are numbered 1 to 8 and placed in a box. One piece of paper is drawn from the box, its number is written.

Algebra 2/Trig Name: ________________________

Sequences, Series, and Probability

Counting Methods and Probability Theory

The Pigeonhole Principle

1. In how many ways can six people sit in a six-passenger car?

Xuan Guo Lab 9 Xuan Guo

Puzzle A Puzzle B.

8.3 Counting Apply the fundamental counting principle

Section 12.8 The Counting Principle and Permutations

NUMBERS one two three four five six seven eight

Counting Methods and Probability Theory

Warm-Up Take out your Unit 1 pretest and complete question #2

Rubric: You will be scored on the following:

CLICK THE NUMBERS IN SEQUENCE

Presentation Title Presentation Title

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

CLICK THE NUMBERS IN SEQUENCE

Counting Methods and Probability Theory

Counting Methods and Probability Theory

§4.2, Number Bases in Positional Systems

+/- Numbers Year 3-4 – Addition and subtraction of hundreds within

Presentation transcript:

Pre-Calculus Section 8.6A Counting Principles

1. Eight pieces of paper are numbered 1 to 8 and placed in a box. One piece of paper is drawn from the box, its number is written down, and the piece of paper is returned to the box. Then, a second piece of paper is drawn from the box and its number is written down. Finally, the two numbers are added together. In how many different ways can a sum of 12 occur?

2. Eight pieces of paper are number from 1 to 8 and placed in a box. Two pieces of paper are drawn from the box at the same time, and the numbers on the paper are written down and totaled. In how many ways can a sum of 12 occur?

Fundamental Counting Principal

3. How many different pairs of letters from the English alphabet are possible?

4. Telephone numbers in the United States currently have 10 digits. The first three are the area code and the next seven are the local telephone number. How many different telephone numbers are possible within each area code? (Note that at this time a local telephone number cannot begin with a 0 or 1)

5. Determine the number of ways in which a computer can randomly generate an integer that is divisible by 4 from the numbers 1 through 12.

6. A customer can choose from one of four amplifiers, one of six compact disc players, and one of five speaker models for an entertainment system. Determine the number of possible system configurations.

7. In 1963 the US Postal Service launched the Zoning Improvement Plan (ZIP) Code to streamline the mail-delivery system. A ZIP code consists of a five-digit sequence of numbers. a) find the number of ZIP codes consisting of five digits.

7. In 1963 the US Postal Service launched the Zoning Improvement Plan (ZIP) Code to streamline the mail-delivery system. A ZIP code consists of a five-digit sequence of numbers. b) find the number of ZIP codes consisting of five digits, if the first digit is a 1 or 2.