11-1 Permutations and Combinations
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1 Fundamental Counting Principal 11-1 Permutations and Combinations Using the Fundamental Counting Principle 1a. A make-your-own-adventure story lets you choose 6 starting points, gives 4 plot choices, and then has 5 possible endings. How many adventures are there? 1b. A password is 4 letters followed by 1 digit. Uppercase letters (A) and lowercase letters (a) may be used and are considered different. How many passwords are possible? Permutation n Factorial For any whole number n, Words Numbers Algebra Permutations Numbers Algebra Finding Permutations 2a. Awards are given out at a costume party. How many ways can Most Creative, Silliest, and Best costume be awarded to 8 contestants if no one gets more than one award? 2b. How many ways can a 2-digit number be formed by using only the digits 5-9 and by each digit being used only once.
2 Combination Combinations Numbers Algebra Application 3. The swim team has 8 swimmers. Two swimmers will be selected to swim in the first heat. How many ways can the swimmers be selected. Q: How can you tell when a factorial is enthusiastic? A: It s always enthusiastic it has an exclamation point!
3 11-2 Theoretical and Experimental Probability Probability Outcome Sample space Event Equally likely outcomes Favorable outcomes Theoretical probability Theoretical Probability Finding Theoretical Probability A red number cube and a blue number cube are rolled. If all numbers are equally likely, what is the probability of each event. 1a. The sum is 6. 1b. The difference is 6. 1c. The red cube is greater. Complement Complement Application 2. Two integers from 1 to 10 are randomly selected. The same number may be chosen twice. What is the probability that both numbers are less than 9? Finding Probability with Permutations or Combinations 3. A DJ randomly selects 2 of 8 ads to play before her show. Two of the ads are by a local retailer. What is the probability that she will play both of the retailer s ads before he show?
4 Geometric probability Finding Geometric Probability 4. Find the probability that a point chosen at random inside the large triangle is in the small triangle. Experiment Trial Experimental probability Experimental Probability Finding Experimental Probability 5. The table shows the results of choosing one card from a deck of cards, recording the suit, and then replacing the card. 5a. Find the experimental probability of choosing a diamond. 5b. Find the experimental probability of choosing a card that is not a club. Sue: My chances of winning are 1 in 10! Bill: Your chances of NOT winning are 9 in 10. Sue: Go away! Bill: Some people can t take a complement.
5 Independent events 11-3 Independent and Dependent Events Probability of Independent Events Finding the Probability of Independent Events Find each probability. 1a. rolling a 6 on one number cube and a 6 on another number cube 1b. tossing heads, then heads, and then tails when tossing a coin 3 times Dependent events Conditional probability Probability of Dependent Events Finding the Probability of Dependent Events Two number cubs are rolled one red and one black. Explain why the events are dependent, and then find the indicated probability. 2. The red cube shows a number greater than 4, and the sum of greater than 9.
6 Using a Table to Find Conditional Probability Find each probability using the table on p a. that a voter from Travis county voted for someone other than George Bush or John Kerry 3b. that a voter was from Harris county voted for George Bush Determining Whether Events are Independent or Dependent A bag contains 10 beads 2 black, 3 white, and 5 red. A bead is selected at random. Determine whether the events are independent or dependent. Find the indicated probability. 4a. selecting a white bead, replacing it, and then selecting a red bead 4b. selecting a white bead, not replacing it, and then selecting a red bead 4c. selecting 3 non-red beads without replacement. Q: What did the IRS couple consider the birth of their new baby? A: A dependent event
7 Binomial Theorem 11-6 Binomial Distributions Expanding Binomials Use the Binomial Theorem to expand each binomial. 1a. x y 5 1b. a + 2b 3 Binomial experiment Binomial Probability Finding Binomial Probabilities 2a. Students are assigned randomly to 1 of 3 guidance counselors. What is the probability that Counselor Jenkins will get 2 of the next 3 students assigned? 2b. Ellen takes a multiple-choice quiz that has 5 questions, with 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing.
8 Problem Solving Application 3a. Wendy takes a multiple-choice quiz that has 20 questions. There are 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing? 3b. A machine has a 98% probability of producing a part within acceptable tolerance levels. The machine makes 25 parts an hour. What is the probability that there are 23 or fewer acceptable parts? To escape the Great Plague in England in 1665, 23 year-old Isaac Newton stayed at his family s country home for 18 months. During that time, he developed his proof of the binomial theorem and made several other important discoveries.
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