Chapter 10 Review day 1

1. Chapter 10 Review day 1 Content Objectives: Students will review for the counting and probability test. Language Objectives: Students will practice problems in their notes, discuss in pairs, decide on an answer, and then confirm their answers on white boards to review for the counting and probability test.

2. Fundamental counting principle • If one event can occur m ways and another event can occur n ways, then the number of ways that both events can occur is m * n. • If multiple events, then multiply the ways together.

3. Permutations • Use permutations when order does matter. • Ex. the song list on a CD, competing in a competition and coming in certain places

4. Combinations • Use when the order doesn’t matter. • Ex. a 5 card hand, choosing students to play on a soccer team.

5. Pascal’s Triangle

6. Binomial Theorem • To expand binomials or find a certain term in the binomial expansion

7. Probability and odds • Probability – Number of outcomes in event A Total number of outcomes • Odds – • Odds in favor of event A – Number of outcomes in A Number of outcomes not in A • Odds against event A– Number of outcomes not in A Number of outcomes in A

8. Independent vs. dependent events • Independent events – two events that don’t effect each other • Dependent events – two events that do effect each other

9. Determine whether to use permutations or combinations • A photographer lines up the 15 members of a family in a single line in order to take a photograph. How many different ways can the photographer arrange the family members for the picture?

10. Determine whether to use permutations or combinations • Five representatives from a senior class of 280 students are to be chosen for the student council. In how many ways can students be chosen to represent the senior class on the student council?

11. Determine whether to use permutations or combinations • A Spanish club is electing a President, vice president, and secretary. The club has 9 members who are eligible for these offices. How many different ways can the 3 offices by held?

12. Determine whether to use permutations or combinations • A relay race has a team of 4 runners who run different parts of the race. There are 20 students on your track squad. In how many ways can the coach select students to compete on the relay team?

13. Determine whether to use permutations or combinations • The window of a music store has 8 stands in fixed positions where instruments can be displayed. In how many ways can 3 identical guitars, 2 identical keyboards, and 3 identical violins be displayed?

14. Determine whether to use permutations or combinations • A group of 15 high school students is volunteering at a local fire station. Of these students, 5 will be assigned to wash fire trucks, 7 will be assigned to repaint the station’s interior, and 3 will be assigned to do maintenance on the station’s exterior. Calculate the number of possible job assignments.

15. The store has the option of 4 shirts, 5 pants, and 3 pairs of shoes. How many choices are there of 1 shirt, 1 pant, and 1 pair of shoes?

16. 8 People are entered in a competition. In how many ways can the first three places come out?

17. Find the number of permutations

18. Find the number of distinguishable permutations of the letters honest.

19. Find the number of combinations

20. You own 12 movies and are taking 5 of them on a car ride. In how many ways can you choose 5 movies from the 12?

21. Expand

22. A card is drawn from a standard deck of playing cards. Find the probability that it is a face card (J,Q,K).

23. A bag of marbles contains 5 green marbles, 3 yellow marbles, and 8 blue marbles. Without looking you draw out a marble, return it, and draw out a second marble. What is the probability that the first marble is green and the second marble is blue

24. A bag of skittles contains 3 yellow skittles, 5 red skittles, and 6 green skittles. One skittle is drawn at random and eaten. Then a second skittle is drawn. What is the probability that the first skittles is green and the second one is red?

25. How many terms does the binomial expansion of contain?

26. Cheryl needs to create a password. She wants to use an arrangement of the first 2 letters of her first name, followed by arrangements of 3 digits of 1978, the year of her birth. How many different passwords can she create this way?

27. A teacher randomly distributes 14 red markers and 6 green markers. What is the probability that the first marker will be red and the second marker will be green?

28. On a certain day the chance of rain is 70% in Oregon and 30% in los angeles. What is the probability that it will not rain in either city?

29. From a group of five boys and six girls, a boy and a girl will be selected to attend a conference. In how many possible ways can the selection by made?

30. A card is drawn from a standard deck of playing cards. Find the probability that it is a face card (J,Q,K).

31. A bag of marbles contains 5 green marbles, 3 yellow marbles, and 8 blue marbles. Without looking you draw out a marble, return it, and draw out a second marble. What is the probability that the first marble is green and the second marble is blue

32. A bag of skittles contains 3 yellow skittles, 5 red skittles, and 6 green skittles. One skittle is drawn at random and eaten. Then a second skittle is drawn. What is the probability that the first skittles is green and the second one is red?

33. How many terms does the binomial expansion of contain?

34. Cheryl needs to create a password. She wants to use an arrangement of the first 2 letters of her first name, followed by arrangements of 3 digits of 1978, the year of her birth. How many different passwords can she create this way?

35. A teacher randomly distributes 14 red markers and 6 green markers. What is the probability that the first marker will be red and the second marker will be green?

36. On a certain day the chance of rain is 70% in Oregon and 30% in los Angeles. What is the probability that it will not rain in either city?

37. From a group of five boys and six girls, a boy and a girl will be selected to attend a conference. In how many possible ways can the selection by made?

38. The state of California uses 7 digits for the license plates assigned to vehicles. How many different license plates can be made (a) with repetition, and (b) without repetition if the first digit is a number, the next three digits are letters, and the last three digits are numbers?

39. Expand.

40. Expand.