Counting principles (33 problems)

Five items are to be randomly selected from the first 50 items on an assembly line to determine the defect rate. How many different samples of 5 items can be chosen?

(Hint: Order is not important)

Compute (a) (b) (c) (d)

To emphasize the importance of correct shelving of books, a librarian tells a group of students the number of possible orders in which just six books may be placed on a shelf. What is that number?

Following are age and sex data for 20 midlevel managers at a service company:

34 F, 49 M, 27 M, 63 F, 33 F, 29 F, 45 M, 46 M, 30 F, 39 M, 42 M, 30 F, 48 M, 35 F, 32 F, 37 F, 48 F, 50 M, 48 F, 61 F.

A manager must be chosen at random to serve on a companywide committee that deals with personnel problems. What is the probability that the chosen manager will be either a woman or over 50 years old or both? Solve both directly from the data and by using the law of unions. What is the probability that the chosen manager will be under 30?

You draw two cards from a standard deck of 52 cards and do not replace the first card before you draw the second.

a) What is the probability that the first card is a king of diamonds and the second is the king of hearts?

b) What is the probability that the first card is a kind of diamonds and the second card is a diamond?

c) What is the probability that the first card is not a king and the second card is also not a king?

Compute

a) P_9,3

b) C_6,2

c) P_5,5

d) C_3,0

A tax accountant has three choices for the method of treating one of a client's deductions. After this choice has been made, there are only two choices for how a second deduction can be treated. What is the total number of possibilities for the treatment of the two deductions?

How many ways can a hand of 6 clubs can be chosen from an ordinary deck?

Compute P_8,3

Calculate the permutation

Compute

In the Cash Now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousand dollars, and the third prize is ten thousand dollars. Use the permutations rule to determine the total number of different ways the winners can be drawn. (Assume that the tickets are not replaced after they are drawn).

How many ways can a committee of 3 men and 4 women can be formed from a group of 10 men and 10 women?

There are 6 balls in an urn. They are identical except for color. Two are red, three are blue, and one is yellow. You are to draw a ball from the urn, note its color, and set if aside. Then you are to draw another ball from the urn and note the color.

(a) Make a tree diagram and note to show all possible outcomes of the experiment. Label the probability associated with each stage of the experiment on the appropriate experiment.

(b) Probability extension: compute the probability for each outcome of the experiment.

A representative of the Environmental protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?

a) There are 11 students participating in a spelling bee. How many ways can the students who go first, second, third, and fourth be chosen?

b) A committee is to consist of two members. If there are seven men and six women available to serve on the committee, how many different committees can be formed?

Compute C_8,3