Combinations Problems Problem 1: Sometimes we can use several counting techniques in the same problem, such as combinations and the addition principle.

Slides:

Advertisements

Similar presentations

Combinations Examples

Advertisements

15.7 Probability Day 3. There are 2 nickels, 3 dimes, and 5 quarters 1.) Find the probability of selecting 1 nickel, 1 dime, and 1 quarter in that order.

Index Student Activity 1: Questions to familiarise students with the

12-1 and 12-2 Permutations and Combinations Get out that calculator!!

Describing Probability

PERMUTATIONS AND COMBINATIONS M408 – Probability Unit.

1 Counting Rules. 2 The probability of a specific event or outcome is a fraction. In the numerator we have the number of ways the specific event can occur.

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.

1 Counting Rules. 2 The probability of a specific event or outcome is a fraction. In the numerator we have the number of ways the specific event can occur.

1 Probability Parts of life are uncertain. Using notions of probability provide a way to deal with the uncertainty.

UNR, MATH/STAT 352, Spring Radar target detection How reliable is the signal on the screen? (Is it a target of a false alarm?)

Laws of Probability What is the probability of throwing a pair of dice and obtaining a 5 or a 7? These are mutually exclusive events. You can’t throw.

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

VOCABULARY  Deck or pack  Suit  Hearts  Clubs  Diamonds  Spades  Dealer  Shuffle  Pick up  Rank  Draw  Set  Joker  Jack 

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

What are the chances of that happening?. What is probability? The mathematical expression of the chances that a particular event or outcome will happen.

Refreshing Your Skills for Chapter 10.  If you flip a coin, the probability that it lands with heads up is 1/2.  If you roll a standard die, the probability.

Permutations and Combinations. Random Things to Know.

12.1 The Counting Principle. Vocabulary  Independent Events: choice of one thing DOES NOT affect the choice of another  Dependent Events: choice of.

Permutations Counting Techniques, Part 1. Permutations Recall the notion of calculating the number of ways in which to arrange a given number of items.

Permutations and Combinations

3.8 Counting Techniques: Combinations. If you are dealt a hand in poker (5 cards), does it matter in which order the cards are dealt to you? A  K  J.

Compound Probability Pre-AP Geometry. Compound Events are made up of two or more simple events. I. Compound Events may be: A) Independent events - when.

Algebra II 10.2: Use Combinations Quiz : Friday, 12/13.

Probability Review. I can… Solve Permutation and Combination problems 15 C 314 P 8 #8 455 #

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.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.2 Theoretical Probability

-2 Combinations. Combination-order doesn’t matter; can have repition or not Graphing calculator n#,math,PRB 3,r#,enter.

Combinations.  End-in-mind/challenge  Sonic advertises that they have over 168,000 drink combinations. Is this correct? How many do they actually have?

S.CP.A.1 Probability Basics. Probability - The chance of an event occurring Experiment: Outcome: Sample Space: Event: The process of measuring or observing.

Do Now: Review 10.4 Multiple Choice 1.) What does mean? a.) b.) c.) Short Answer 2.) Find the number of arrangements of 3 #’s for a locker with a total.

Chapter  Determine how many different possibilities are possible:  1. There are 3 different ice cream flavors and 5 different toppings. You.

Unit 6 Games. The Difference Game Materials –4 decks of cards number –40 pennies One player shuffles the number cards and places them with the numbers.

15.3 Counting Methods: Combinations ©2002 by R. Villar All Rights Reserved.

Algebra 2 Thursday Today, we will be able to… Find the probability of two independent events Find the probability of two dependent events Find.

Quiz 10-1, Which of these are an example of a “descrete” set of data? 2.Make a “tree diagram” showing all the ways the letters ‘x’, ‘y’, and ‘z’

Homework Homework due now. Reading: relations

Name the United States Coins Count the Pennies 10 ¢

Review Homework pages Example: Counting the number of heads in 10 coin tosses. 2.2/

Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 1.They are all red ? 2.At least one is black ? 3.They are.

Permutations, Combinations, and Counting Theory

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.

Algebra-2 Counting and Probability. Quiz 10-1, Which of these are an example of a “descrete” set of data? 2.Make a “tree diagram” showing all.

Introduction to Counting. Why a lesson on counting? I’ve been doing that since I was a young child!

Have you ever played a game where everyone should have an equal chance of winning, but one person seems to have all the luck? Did it make you wonder if.

Multiplication Counting Principle How many ways can you make an outfit out of 2 shirts and 4 pants? If there are m choices for step 1 and n choices for.

C OUNTING P RINCIPLE Warm UP: List down what make up of a deck of cards. Name what you know about a deck of cards.

Expected Value and Fair Game S-MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). S-MD.7 (+) Analyze.

Question #1 A bag has 10 red, 3 yellow, and 5 blue marbles. You pick one. What is the probability that you select a blue marble?

Combinations 0.4. Combinations: a selection of r objects from a group on n objects where the order is not important.

The Counting Principle Permutation Or Combination.

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

Sample Spaces and Probability Addition Rules Multiplication Rules and Conditional Probability Counting Rules Probability and Counting Rules

Probability Distributions. Constructing a Probability Distribution Definition: Consists of the values a random variable can assume and the corresponding.

Quiz: Draw the unit circle: Include: (1)All “nice” angles in degrees (2) All “nice” angles in radians (3) The (x, y) pairs for each point on the unit circle.

Arrangements and Selections (and how they may be counted)

Permutations and Combinations

11.9: Solving Probability Problems by Using Combinations

Combinations Problems

Section Combinations (with and without restrictions)

The Addition Rule.

BASIC PROBABILITY Probability – the chance of something (an event) happening # of successful outcomes # of possible outcomes All probability answers must.

Permutations and Combinations

Name the United States Coins

Section 12.2 Theoretical Probability

Section 12.2 Theoretical Probability

Section 12.2 Theoretical Probability

Vocabulary FCP/ Comb/Perm Simple Probability Compound Probability 1

Presentation transcript:

Combinations Problems Problem 1: Sometimes we can use several counting techniques in the same problem, such as combinations and the addition principle. Say you are buying a sundae with one scoop of vanilla ice cream, and you have a choice of up to 3 toppings. In how many ways can you select your toppings? (Hint: Calculate the number of ways to choose no topping, C(3, 0), the number of ways to choose 1 topping, C(3, 1), 2 toppings, C(3, 2), and 3 toppings, C(3, 3). Then add together all the possibilities.)

Combinations Problems Problem 2: How many combinations are possible for 4 toppings? For 5 toppings? Based on your results, without calculating the answer what would you predict for the number of possible combinations with 6 toppings?

Combinations Problems Problem 3: You are about to take a 10- question true/false quiz. The teacher confides that exactly 3 of the questions are true. a.) In how many ways can you choose 3 questions to answer true? b.) In how many ways can you choose 7 questions to answer false? c.) In how many total possible ways can you answer the quiz, regardless of the teacher’s revelation about 3 questions being true?

Combinations Problems Problem 4: Imagine a state lottery has players choose 6 numbers from the numbers (The order does not matter.) a.) How many unique cards are possible? (One play, or six numbers per card) b.) If a computer could generate 1 card per second, how long would it take to generate all the possible cards? c.) Do you think it would be worthwhile to play every possible card? Why or why not?

Combinations Problems Problem 5: Imagine the same state lottery as in Problem 4 has prizes for matching 3, 4, 5, or 6 out of the 6 chosen numbers. a.) How many unique winning cards are possible? b.) If a player matching 3 numbers wins $5, about how much would you expect a player to win for matching all 6 numbers?

Combinations Problems Problem 6: A pizzeria offers 9 different toppings. A pizza must have a minimum of 1 topping, and can have any combination of toppings up to the maximum of all 9 toppings. Customers also get to choose from among 3 types of crust. How many different pizza varieties are possible?

Combinations Problems Problem 7: A hockey coach is trying to select a starting lineup for the next game. The team has 12 forwards, 6 defensemen, and 2 goalies. The starting lineup will consist of 3 forwards, 2 defensemen, and 1 goalie. How many different groups of 6 players could the coach select to start? (Assume that all 12 forwards are able to play any forward position—left wing, center, or right wing—and all 6 defensemen can play either right or left defense.)

Combinations Problems Problem 8: How many different sums of money could you arrange if you had 1 penny, 1 nickel, 1 dime, and 1 quarter? (Hint: Include all combinations of 1, 2, 3, or 4 coins.)

Combinations Problems Problem 9: A regular deck of cards consists of 4 suits: Hearts and Diamonds are red; Spades and Clubs are black. Each suit has the cards 2-10, as well as a Jack, Queen, King, and Ace. So there are 4 suits of 13 cards each, for a total of 52 cards. a.) How many pairs are possible in a deck of cards? b.) In how many ways could you get 2 pair (e.g., two 4s and two Kings) if you pick 4 cards from a deck?

Combinations Problems Problem 10: A regular deck of cards consists of 4 suits: Hearts and Diamonds are red; Spades and Clubs are black. Each suit has the cards 2-10, as well as a Jack, Queen, King, and Ace. So there are 4 suits of 13 cards each, for a total of 52 cards. In how many ways could you get a flush if you pick 5 cards from a regular deck? (A flush is 5 cards all of the same suit.)