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Permutations, Combinations, and Counting Theory

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

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Warm Up April 22, 2014

Warm Up April 22, 2014. What is the probability that you pull a queen or a king out of a standard deck of cards? What is the probability that you roll a 3 or 10 on two dice?. EOCT Week 14 #2. Compound Probability.

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At a particular carnival, there is a dice game that costs $5 to play.

At a particular carnival, there is a dice game that costs $5 to play. -If the die lands on an odd number, you lose. -If the die lands on a 2 or 4, you win $8. -If the die lands on 6, you win $14. How much could I “walk away with” for each of the possible outcomes?.

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Independent and Dependent Events

Independent and Dependent Events. Unit 6 : Probability. Warm Up. Students in a mathematics class pick a card from a standard deck of 52 cards, record the suit, and return the card to the deck. The results are shown. How many students are in the class?

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M ARIO F . T RIOLA

S TATISTICS. E LEMENTARY. Section 3-4 Multiplication Rule: Basics. M ARIO F . T RIOLA. E IGHTH. E DITION. Finding the Probability of Two or More Selections. Multiple selections means Multiplication Rule. Notation. P(A and B) = P(event A occurs in a first trial and

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Probability

Probability. 13.3 Probability and Odds. Warm Up. What is the probability of rolling a 5 on a die?. What is the probability of drawing a 4 from a deck of playing cards?. 13.3 Probability and Odds. Review. An independent event occurs when the outcome does not affect other events .

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Warm up

Warm up. What is the probability of choosing a red card from a standard deck of cards? What is the probability of choosing a king from a deck of cards? Given that a card is black, what is the probability that you choose a 4?. 50%. 8%. 2 /26 = 8%. Review HW. Probability Tables.

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Section 16.4.1 Probability Problems Solved with Combinations

Section 16.4.1 Probability Problems Solved with Combinations. Pre-Calculus. Probability Solved with Combinations. This is just another method to help simplify calculating probabilities. These problems can be solved in a multitude of ways. However, sometimes they can be quite tedious.

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355 views • 12 slides

Section 11.5

Math in Our World. Section 11.5. Probability Using Permutations and Combinations. Learning Objectives. Compute probabilities using combinations. Compute probabilities using permutations. Events with Large Possibilities.

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Chapter 10

Chapter 10. Counting Techniques. Combinations Section 10.3. Combinations. A selection of distinct objects without regard to order is a combination . Combination Formula. The number of combinations of n objects, taken r at a time(order is not important and n  r ). .

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Experimental Probability

Experimental Probability . Experimental Probability. Probability based on the results of an experiment that actually happened Used to make future predictions. Theoretical vs Experimental. Often times the theoretical and experimental probabilities of the same event are different.

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Chapter 10

Chapter 10. Counting Techniques. Permutations Section 10.2. Permutations. A permutation is an arrangement of n objects in a specific order. Factorial Notation. Factorial Formulas For any counting n. Exercises:. In how many ways can 4 people be seated in a row?.

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Terminologies in Probability

Terminologies in Probability. Experiment – Any process that produces an outcome that cannot be predicted with certainty. Example: tossing a coin, rolling dice, picking a card, doing a survey, conducting experimental studies. Sample Space – Set of all possible outcomes.

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660 views • 8 slides

Chapter 10

Chapter 10. Counting Techniques. Miscellaneous Counting Methods Section 10.4. Permutations and Combinations . Three cards are dealt in succession and without replacement from a standard deck of 52 cards . In how many different orders can the cards be dealt ?

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The Pigeonhole Principle

The Pigeonhole Principle. Section 6. 2. Section Summary. The Pigeonhole Principle The Generalized Pigeonhole Principle. The Pigeonhole Principle. If a flock of 20 pigeons roosts in a set of 19 pigeonholes, one of the pigeonholes must have more than 1 pigeon.

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16.4 Probability Problems Solved with Combinations

16.4 Probability Problems Solved with Combinations. 16.4 Warm Up. Three cards are drawn from a well-shuffled standard deck of 52 cards, one after the other and without replacement. Find the probability of drawing all clubs b) no clubs

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Bell Ringer

Bell Ringer. Solve for x. Round your answer to the nearest whole number. -2(3 + 6v) = -5v – 25 -6 – 12v = -5v – 25 + 6 + 6 -12v = -5v – 19 + 5v + 5v

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5.2 The Pigeonhole Principle

5.2 The Pigeonhole Principle. Theorem 1: The Pigeonhole Principle If k is a positive integer and k+1 or more objects are placed into k boxes, then there is at least one box containing two or more of the objects.

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1.29k views • 5 slides

Playing Cards

Playing Cards. By Ruben Gonzalez. Background.

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This is the question for #1 on the viewing guide.

This is the question for #1 on the viewing guide. You conduct and experiment where you flip a coin three times in a row and record the results. Write all of the possible outcomes of this experiment. HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Probability.

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