This document provides examples of using fundamental counting principles, permutations, and combinations to calculate probabilities. It includes 10 problems calculating probabilities of events like arranging a group of people in different orders, being dealt certain poker hands, selecting lottery numbers, and choosing items from a box where some are defective. The key concepts covered are theoretical, empirical and subjective probability, and determining the total number of possible outcomes versus favorable outcomes to calculate probability.

1. 11.5 Probability with the Fundamental Counting Principles, Permutations and Combinations

2. Three Kinds of Probability Theoretical Probability Empirical Probability Subjective Probability

3. Probability with FCP (Problem # 1) A restaurant offers 3 appetizers (salad, soup, breadsticks), 4 main courses (chicken, beef, fish, pork) and 2 desserts (cake and ice cream). What is the probability of getting a soup, chicken and ice cream for a meal? 1/24

4. Probability with FCP (Problem # 2) Mr. P has 4 ties (Cartoon character, Navy Blue, Black, Striped), 4 shirts (white, blue, black and gray) and 4 pairs of pants (black, brown, beige and gray). What is the probability that he will wear a black tie, black shirt and black pants? 1/64

5. Probability of a Permutation Number of ways the permutation can occur Total number of permutations

6. Probability with Permutations (Problem # 3) Jay-Z, Jeremih, R. Kelly and T.I. were invited to the 50th celebration at Seton. They arrived randomly and each person arrived at different time. In how many ways can they arrive? In how many ways can Jay-Z arrive first and T.I. last? What is the probability that Jay-Z arrive first and T.I. last?

7. Answer: Total Permutation: 4! = 24 No. of permutations for Jay Z to arrive first and T.I. last = 1 x 2 x 1 x 1 = 2 c. Probability = 2/24 = 1/12

8. Probability with Permutations (Problem # 4) Suppose that you want to arrange the 4 Twilight books. What is the probability that Breaking Dawn (the last book in the series) is placed at the end? What is the probability that Twilight (the first book in the series) is placed first and New moon (the second in the series) placed second? 6/24 or ¼ 2/24 or 1/12

9. Probability with Permutations (Problem # 5) Miley Cyrus, Taylor Swift, DemiLovato, Lady GaGa and Kelly Clarkson agree to hold a concert. What is the probability that Lady GaGa will perform first and Kelly Clarkson last? 6/120 = 1/20

10. Probability of a combination Number of ways the combinations can occur Total number of combinations

11. Probability with Combinations (Problem # 6) A poker hand consists of five cards. a. Find the total number of 5-card poker hands. b. A heart flush is a 5-card hand that consists of all hearts. Find the number of possible heart flush. c. Find the probability of being dealt a heart flush? A. Total Combination: 2,598,960 Possible Combination for heart flush: 1287 Probability: 1287/2,598,960

12. Probability with Combinations (Problem # 7) To play the Powerball, a player needs to select five numbers from 1-59 and a powerball number from 1-39. a. What is the chance of winning the top prize if you buy one ticket? b. What is the chance of winning the top prize if the cost for one ticket is $1 and you spent $100? A. 1/195,249,054 B. 50/97,624,527

13. Probability with Combinations (Problem # 8) To play the DC Lotto Hot Sizzler, a player must select 5 numbers from 1-39 and 1 number from 1-19. What is the probability of winning the top prize if you only purchased one ticket? 100 tickets? 1000 tickets? 10,000 tickets? One ticket: 1/10,939,383 1000 tickets: 1000/10,939,383 10,000 tickets: 10,000/10,939,383

14. Probability with Combinations (Problem # 9) A group consists of 6 men and 10 women. Four members are selected at random to attend a conference. Find the probability that the selected group consists of A. All men B. All women C. 2 men and 2 women A. 3/364 B. 3/26 C. 135/364

15. Probability with Combinations (Problem # 10) A box contains 20 IPods, where 5 of them are defective. If 5 are selected at a random, find the probability that A. All are defective B. None are defective A. 1/15504 B. 1001/5168