In a race in which eight automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
2. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?
3. The Senate in a certain state is comprised of 58 Republicans, 39 Democrats, and 3 Independents. How many committees can be formed if each committee must have 3 Republicans and 2 Democrats?
4. You are dealt one card from a standard 52-card deck. Find the probability of being dealt a diamond.
8. A group consists of six men and six women. Five people are selected to attend a conference.
a. In how many ways can five people be selected from this group of twelve?
b. In how many ways can five women be selected from the six women?
c. Find the probability that the selected group will consist of all women.
9. If you are dealt 33 cards from a shuffled deck of 52 cards, find the probability of getting two queens and on king.
10. You are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.
11. You are dealt one card from a 52-card deck. Find the probability that you are dealt a king or a red card.
12. The mathematics department of a college has 6 male professors, 12 female professors, 15 male teaching assistants, and 6 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.
14. A coin is tossed and a die is rolled. Find the probability of getting a tail and a number greater than 1.
17. An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model is $16,000. The probability of being awarded the bid is 0.2, and anticipated profits are $80,000, resulting in a possible gain of this amount minus the $16,000 cost for plans and a model.
a. What is the expected value in this situation?
b. Choose the statement below that best describes what this value means.
A.
In the long run, the architect would expect to break even.
B.
In the long run, the architect would expect to earn this amount.
C.
In the long run, the architect would expect to lose this amount.
D.
None of the above.
18.
A construction company is planning to bid on a building contract. The bid costs the company $1800. The probability that the bid is accepted is ONE FITH. If the bid is accepted, the company will make $51,500 minus the cost of the bid.
a. What is the expected value in this situation?
b. Choose the statement below that best describes what this value means.
A.
In the long run, the construction company would expect to break even on average.
B.
In the long run, the construction company would expect to earn this amount on average per bid.
C.
In the long run, the construction company would expect to lose this amount on average per bid.
D.
None of the above.
19. A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 10 stocks?
20. At a benefit concert, twelve bands have volunteered to perform but there is only enough time for six of the bands to play. How many lineups are possible?
