Fundamental Counting Theorm

Slides:

Advertisements

Similar presentations

Permutations and Combinations

Advertisements

Counting Chapter 13 sec 1. Break up into groups One method of counting is using the tree diagram. ◦ It is useful to keep track of counting. ◦ Order of.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 12.2, Slide 1 12 Counting Just How Many Are There?

Counting Principles The Fundamental Counting Principle: If one event can occur m ways and another can occur n ways, then the number of ways the events.

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?

Sample Space: The Counting Principle By: The Math Ladies.

Warm Up Use an inequality symbol to make each expression true a x 10 4 ___________ 5, 430 b. 32 ÷ ¼ ___________ 32 ÷4 c. 0.72___________¾.

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 :

Permutations and Combinations. Random Things to Know.

Lesson 14.1 Probability and the Basic Counting Principle.

 Samson wants to climb a mountain. He knows that if the slope is over 2, he will fall. Will he fall? (1, 0) (5, 9) m = 9 – 0 9 – = m = 2.25 Samson.

Day 18 Basic Counting Rule. Probabilities Related concepts: Experiment, Event, Sample Space If we assume all sample points are equally likely, the probability.

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

Permutations, Combinations, and Counting Theory AII.12 The student will compute and distinguish between permutations and combinations and use technology.

The Fundamental Counting Principle states that if there are x ways to choose a first item and y ways to choose a second item, then there are x(y) ways.

 Roll a die, flip a coin  Unique 3 letter arrangements of CAT  Unique 4 digit arrangements of 1, 2, 3, 4.

Permutations and Combinations

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

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 12.2, Slide 1 12 Counting Just How Many Are There?

Probability & Statistics The Counting Principle Section 12-1.

Lesson #35 Outcomes and Probability. Probability is used in….

Fundamental Counting Theorm. Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when.

Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three blouses, five pairs of pants and three pairs of shoes to choose.

Permutations, Combinations, and Counting Theory

Counting Principle 1.Suppose you have three shirts (red, black, and yellow) and two pair of pants (jeans and khakis). Make a tree diagram to find the number.

Lesson 0.4 (Counting Techniques)

DAY 6: FUNDAMENTAL COUNTING PRINCIPLE Classwork: pptx examples in class Discrete Pre- Test (not a grade in HAC) Unit 2 Project- Due day 13 Homework (day.

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

Counting Techniques. Multiplication Principle (also called the Fundamental Counting Principle) Combinations Permutations Number of subsets of a given.

October 12, Objectives Content Objectives  Students will review probability rules through review of Thursday’s work.  Students will learn about.

Warm up How many possible pizzas could you make with 3 types of meats, 2 types of cheeses, and 2 types of sauces? 5 * 4 * 3 * 2 * 1 =

Monday, March 31, 2014 AIM: What is the Multiplication Counting Principle?  DO NOW: Kimberly has three pair of pants: one black, one red, and one tan.

Permutations and Combinations

Probability What are the chances of that happening?

A local restaurant is running a lunch special where you can purchase a lunch combo for $5.00. This combo includes a soup, a salad, and a drink. Here are.

12.1 Counting Key Q-How many outcomes can an event have? Fundamental Counting Principle More than one event to take into account. Multiply all events.

INTRO TO COUNTING: 11.4 Day 1. SIMPLE ENUMERATION COLLECTION OF ITEMS THAT IS A COMPLETE, ORDERED LISTING OF ALL OF THE ITEMS IN THAT COLLECTION. How.

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 Review Plus a little Dry Run, Sorting and Code.

Permutations and Combinations

A ratio that measures the chance that an event will happen

Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three shirts, five pairs of pants and three pairs of shoes to choose.

The Counting Principle

Calculating Probability, Combinations and Permutations

Permutations and Combinations

Set, Combinatorics, Probability & Number Theory

Counting – Learning Outcomes

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Lesson 11-1 Permutations and Combinations

Permutations and Combinations

Probability Jeopardy Definition 100 TP/EP/Ind/Dep 100 Counting 100

Permutations and Combinations

Probability Jeopardy Definition 100 TP/EP/Ind/Dep 100 Counting 100

How many possible outcomes can you make with the accessories?

Counting Principle.

The Multiplication Principle

Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three blouses, five pairs of pants and three pairs of shoes to choose.

Bellwork Practice Packet 10.3 B side #3.

Permutations and Combinations

Permutations and Combinations

Lecture 7: Permutations and Combinations

Warm Up Melanie is choosing an outfit for a job interview. She has four dresses, three blouses, five pairs of pants and three pairs of shoes to choose.

Permutations and Combinations

Presentation transcript:

Fundamental Counting Theorm

Fundamental Counting Principle Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more characteristics . Fundamental Counting Principle states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are m* n possible outcomes for the two events together.

Fundamental Counting Principle Lets start with a simple example. A student is to roll a die and flip a coin. How many possible outcomes will there be? 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T 12 outcomes 6*2 = 12 outcomes

Fundamental Counting Principle For a college interview, Robert has to choose what to wear from the following: 4 slacks, 3 shirts, 2 shoes and 5 ties. How many possible outfits does he have to choose from? 4*3*2*5 = 120 outfits

Now you try! A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there? Rob has 4 shirts, 3 pairs of pants, and 2 pairs of shoes that all coordinate. How many outfits can you put together? Grace loves to eat salad! How many salads can she put together if she can pick out one type of lettuce from 2 choices, one vegetable from 4 choices and one dressing from 7 choices? How many 5-digit numbers can be formed (using 0 – 9)? How many 5-digit numbers can be formed if each one uses all the digits 0, 1, 2, 3, 4 without repetition?

Closure In how many ways can 6 bicycles be parked in a row?