How many different 4 letter radio station

1. Do this problem using permutation:

You have 5 math books and 6 history books to put on a shelf with five slots. In how many ways can you put the books on the shelf if the first two slots are to be filled with the books of one subject and the next three slots are to be filled with the books of the other subject?

2. Do this problem using combination:

In how many ways can a person choose to vote for three out of five candidates on a ballot for a school board election?

3. Find the number of different ways to draw a 5-card hand from a deck to have the following combinations.

1. Three face cards.

1. A heart flush (all hearts).

1. Two hearts and three diamonds.

1. Two cards of one suit, and three of another suit.

1. Two kings and three queens.

1. Two cards of one value and three of another value.

4. Do this problem using a tree diagram or multiplication axiom.

How many different 4-letter radio station call letters can be made if the first letter must be K or W and none of the letters may be repeated?

5. Find the number in this set:

In a survey of computer users, it was found that 50 use HP printers, 30 use IBM printers, 20 use Apple printers, 13 use HP and IBM, 9 use HP and Apple, 7 use IBM and Apple, and 3 use all three. How many use at least one of these Brands?

6. List the elements of this set:

Let Universal set=U={1,2,3,4,5,6,7,8,9,10}, A={1,2,3,4,5}, B={1,3,4,6}, and C={2,4,6}.

List the members of the following sets.

A ∪ B

A ∩ C

A ∪ B ’ ∩ C

A ’ ∪ B ∩ C ’

7. Solve using the graphical method. Choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all corner points, and determine the solution that optimizes the objective function.

Dr. Lum teaches part-time at two different community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class taught by him at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers, and for each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $4,000 per class at Hilltop College and $5,000 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?

8. * Use a tree diagram solving this problem:

The Long Life Light Bulbs claims that the probability that a light bulb will go out when first used is 15%, but if it does not go out on the first use the probability that it will last the first year is 95%, and if it lasts the first year, there is a 90% probability that it will last two years. What is the probability that a new bulb will last two years?

9. Do this problem using the expected value concepts.

During her four years at college, Niki received A's in 30% of her courses, B's in 60% of her courses, and C's in the remaining 10%. If A=4, B=3, and C=2, find her grade point average.

10. John's probability of passing statistics is 40%, and Linda's probability of passing the same course is 70%. If the two events are independent, find the following probabilities.

1. P(both of them will pass statistics)

1. P(at least one of them will pass statistics)

11. CONDITIONAL PROBABILITY

Do this problem using the conditional probability formula: P(A∣B)=P(A∩B)P(B).

At De Anza College, 20% of the students take Finite Math, 30% take History, and 5% take both Finite Math and History. If a student is chosen at random, find the following conditional probabilities.

1. Student is taking Finite Math given that said student is taking History.

1. Srudent is taking History given that said student is taking Finite Math.

12. MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE

Determine whether the following pair of events are mutually exclusive.

1. A = {A person earns more than $25,000} B = {A person earns less than $20,000}

1. A card is drawn from a deck: C = {It is a King} D = {It is a heart}

1. A single, fair, 6-sided die is rolled: E = {An even number shows} F = {A number greater than 3 shows}

13. A jar contains four marbles numbered 1, 2, 3, and 4. If two marbles are drawn, find the following probabilities.

a. P (the sum of the number is 5)

b. P (the sum of the numbers is odd)

c. P (the sum of the numbers is 9)

d. P (one of the numbers is 3)

14. * The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. The following table shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students.

Seasons

Number of students

Proportion of Population

Spring

8

24%

Summer

9

26%

Fall

11

32%

Winter

6

18%

15. *NORMAL APPROXIMATION TO BINOMIAL

Suppose you have a normal distribution with a mean of 6 and a standard deviation of 1. What is the probability of getting a Z score of exactly 1.2?

16. *Solve the given linear programming problem graphically:

Nutrition: A dietitian is to prepare two foods to meet certain requirements. Each pound of Food I contains 100 units of vitamin C, 40 units of vitamin D, and 10 units of vitamin E and costs 20 cents. Each pound of Food II contains 10 units of vitamin C, 80 units of vitamin D, and 5 units of vitamin E and costs 15 cents. The mixture of the two foods is to contain at least 260 units of vitamin C, at least 320 units of vitamin D, and at least 50 units of vitamin E. How many pounds of each type of food should be used to minimize the cost?