1. A combination is an ordered arrangement of objects.  
   {#1}
   
   
2. The number of different ordered arrangements of «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» distinct objects is «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»!«/mo»«/math»
   
   {#2}
   
   
3. If you devide the number of permutaions of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.  
   
   {#3}
   
   
4. «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mn»5«/mn»«none/»«mprescripts/»«mn»7«/mn»«none/»«/mmultiscripts»«mo»=«/mo»«mmultiscripts»«mi»C«/mi»«mn»2«/mn»«none/»«mprescripts/»«mn»7«/mn»«none/»«/mmultiscripts»«/math»   
   {#4}

Space shuttle astronauts each consume an average of 3000 calories per day.  One meal normally consists of a main dish, a vegetable dish, and two different desserts.  The astronauts cam choose from #a main dishes, #b vegetable dishes, and #c desserts.  How many different meals are possible?

#a people compete in a downhill ski race.  Assuming that there are no ties, in how many different orders can the skiers finish?

In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security code?

The starting lineup for a softball team consists of ten players.  How many different batting orders are possible using the starting lineup?

A Lottery has #a numbers. In how many different ways can #b of the numbers be selected?  (Assume that the order of selection is not important.)

There are #a processes involved in assembling a certain product.  These processes can be performed in order.  Management wants to find which order is the least time-consuming.  How many different orders will have to be tested?

A landscaper wants to plant #a oak trees, #b maple trees. and #c poplar trees along the border of a lawn.  The trees are to be spaced evenly apart.  In how many distinguishable ways can they be planted?

In order to conduct an experiment, #a subjects are randomly selected from a group of #b subjects.  How many different groups of #a subjects are possible?

In how many distinguishable ways can the letters in the word statistics be written?

From a group of #n people, a jury of #r people is selected.  In how many different ways can a jury of #r people be selected?

palmes

1. Find the number of distinguishable ways the letters can be arranged.
   {#1}
   
   
2. There is one arrangement that spells an inportant term used throughout the course.  Find the term.
   {#2}
   
   
3. If the letters are randomly arranged in order, what is the probability that the arrangement spells the word from part b.
   {#3}

nevte

1. Find the number of distinguishable ways the letters can be arranged.
   {#1}
   
   
2. There is one arrangement that spells an inportant term used throughout the course.  Find the term.
   {#2}
   
   
3. If the letters are randomly arranged in order, what is the probability that the arrangement spells the word from part b.
   {#3}

etre

1. Find the number of distinguishable ways the letters can be arranged.
   {#1}
   
   
2. There is one arrangement that spells an inportant term used throughout the course.  Find the term.
   {#2}
   
   
3. If the letters are randomly arranged in order, what is the probability that the arrangement spells the word from part b.
   {#3}

ediman

1. Find the number of distinguishable ways the letters can be arranged.
   {#1}
   
   
2. There is one arrangement that spells an inportant term used throughout the course.  Find the term.
   {#2}
   
   
3. If the letters are randomly arranged in order, what is the probability that the arrangement spells the word from part b.
   {#3}

unoppolati

1. Find the number of distinguishable ways the letters can be arranged.
   {#1}
   
   
2. There is one arrangement that spells an inportant term used throughout the course.  Find the term.
   {#2}
   
   
3. If the letters are randomly arranged in order, what is the probability that the arrangement spells the word from part b.
   {#3}

sidtbitoiurn

1. Find the number of distinguishable ways the letters can be arranged.
   {#1}
   
   
2. There is one arrangement that spells an inportant term used throughout the course.  Find the term.
   {#2}
   
   
3. If the letters are randomly arranged in order, what is the probability that the arrangement spells the word from part b.
   {#3}

A horse race has #a entries.  Assuming that there are no ties, what is the probability that the tree horses owned by one person finish first, second, and third?

A pizza shop offers #t.  No topping can be used more than once.  What is the probability that the toppings on the pizza are pepperoni, onions, and mushrooms?

You look over the songs on a jukebox and determine that you like #r of the #n songs.

1. What is the probability that you like the next #a songs that are played?  Assume a song cannot be repeated.
   {#1}
   
   
2. What is the probability that you do not like the next #a songs that are played?  Assume a song cannot be repeated.
   {#2}

The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of #n candidates.  Six of the candidates are members of the debate team.

1. What is the probability that all of the offices will be filled by members of the debate team?
   {#1}
   
   
2. What is the probability that none of the offices are filled by members of the debate team?
   {#2}

1. there are no restrictions?
   {#1}
   
   
2. the selection must include a sales representative from each region?
   {#2}
   
   
3. What is the probability that the four sales representatives chosen to participate in the training program will be from only two of the four regions if they are chosen at random?
   {#3}

In a certain state, each automobile license plate number consists of #a letters followed by a #b-digit number.  How many distinct license plate numbers can be formed if:

1. there are no restrictions?
   {#1}
   
   
2. the letters O and I are not used?
   {#2}
   
   
3. What is the probability of selecting at randoma license plate that ends in an even number?
   {#3}

A password consists of #a letters followed by a #b-digit number.  How many passwords are possible if:

1. there are no restrictions?
   {#1}
   
   
2. none of the letters or digits can be repeated?
   {#2}
   
   
3. What is the probability of guessing the password in one trial if there are no restrictions?
   {#3}

An ares code consists of three digits.  How many area codes are possible if:

1. there are no restrictions?
   {#1}
   
   
2. the first digit cannot be a 1 or a 0?
   {#2}
   
   
3. What is the probability of selecting an area code at random that ends in an odd number if the first digit cannot be a 1 or a 0.
   {#3}

In how many orders can #a broken computers and #b broken printers be repaired if:

1. there are no restrictions?
   {#1}
   
   
2. the printers must be repaired first?
   {#2}
   
   
3. the computers must be repaired first?
   {#3}
   
   
4. If the order of repairs has no restrictions and the order of repairs is done at random, what is the probability that a printer will be repaired first?
   {#4}

A shipment of #a microwave ovens contains #b defective units.  In how many ways can a restaurant buy three of these units and recieve:

1. no defective units?
   {#1}
   
   
2. one defective unit?
   {#2}
   
   
3. at least two nondefective units?
   {#3}
   
   
4. What is the probability of the restaurant buying at least two defective units?
   {#4}

In a state lottery, you must select #r numbers (in any order) out of #n correctly to win the top prize.

1. How many ways can 5 numbers be chosen from 40 numbres?
   {#1}
   
   
2. You purchase one lottery ticket.  What is the probability of winning the top prize?
   {#2}

A company that has #n employees chooses a committee of #r to represent employee retirement issues.  When the committee was formed, none of the #m minority employees were selected.

1. Find the number of ways #r employees can be chosen from #n.
   {#1}
   
   
2. Find the number of ways #r employees can be chosen from #b nonminorities.
   {#2}
   
   
3. If the committee was chosen randomly (without bias), what is the probability that it contained no minorities?
   {#3}
   
   
4. Does your answer to part 3 indicate that the committee selection was biased?
   {#4}

You are dealt a hand of five cards from a standard deck of playing cards.  Find the probability of being dealt a hand consisting of:

1. four-of-a-kind.
   {#1}
   
   
2. a full house which consists of 1 three-of-a-kind and 1 two-of-a-kind.
   {#2}
   
   
3. three-of-a-kind.  (The other cards are different from each other.)
   {#3}
   
   
4. two clubs and one of each other suits.
   {#4}

1. all first-shift workers.
   {#1}
   
   
2. all second-shift workers.
   {#2}
   
   
3. six first-shift workers.
   {#3}
   
   
4. four second-shift workers.
   {#4}

1. two events that are mutually exclusive.
2. two events that are not mutually exclusive.

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«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mi»A«/mi»«mo»§#160;«/mo»«mtext»or«/mtext»«mo»§#160;«/mo»«mi»B«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mi»P«/mi»«mfenced»«mi»A«/mi»«/mfenced»«mo»+«/mo»«mi»P«/mi»«mo»(«/mo»«mi»B«/mi»«mo»)«/mo»«/math»

1. 
   {#1}
   
   
2. 
   {#2}

Event A: Randomly select a female worker.
Event B: Randomly select a worker with a college degree.
{#1}

Event A: Randomly select a member of U.S. Congress.
Event B: Randomy select a male U.S. Senator.
{#2}

Event A: Randomly select a person between 18 and 24 years old.
Event B: Randomly select a person between 25 and 34 years old.
{#3}

Event A: Randomly select a person between 18 and 24 years old.
Event B: Randomly select a person earning between $20,000 and $29,999.
{#4}

1. Are the events "selecting a week that contained overtime wages" and "selecting a week that contained temporary help wages" mutually exclusive?  {#1}
2. If an auditor randomly examined the payroll records for only one week, what is the probability that the payroll for that week contained overtime wages or temporary help wages?
   {#2}

1. Are the events "selecting a woman student" and "selecting a business major" mutually exclusive?  {#1}
2. If the college newspaper conducts a poll and selects students at random to answer a survey, find the probability that a selected student is a woman or a business major.  {#2}

1. Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" mutually exclusive?  {#1}
2. If a quality control inspector randomly selects a carton, find the probability that the carton has a puncture or a smashed corner.  {#2}

1. Are the events "selecting a can without a puncture" and "selecting a can without a smashed edge" mutually exclusive?  {#1}
2. If a quality inspector randomly selects a can, find the probability that the can does not have a puncture or does not have a smashed edge.  {#2}

1. Randomly selecting a diamond or a 7  {#1}
2. Randomly selecting a red suit or a queen  {#2}
3. Randomly selecting a 3 or a face card  {#3}

1. Rolling a 6 or a number greater than 4  {#1}
2. Rolling a number less than 3 or an even number  {#2}
3. Rolling a 3 or an even number  {#3}

1. Randomly selecting someone under five years old  {#1}
2. Randomly selecting someone who is not 65 or older  {#2}
3. Randomly selecting someone who is between 18 and 34 years old  {#3}

1. Randomly selecting a car with two occupants  {#1}
2. Randomly selecting a car with two or more occupants  {#2}
3. Randomly selecting a car with between two and five occupants, inclusive  {#3}

1. Randomly selecting a person from the sample who is not completely satisfied with the quality of education  {#1}
2. Randomly selecting a person from the sample who is somewhat dissatisfied or completely dissatisfied with the quality of education  {#2}

1. Randomly selecting a person from the sample who feels the biggest  problem with the movies is that movies are not as good as they used to be  {#1}
2. Randomly selecting a person from the sample who feels the biggest problem with the movies is not that movies have too much violence or that the tickets cost too much  {#2}

1. The student is male or a nursing major.  {#1}
2. The student is female or not a nursing major.  {#2}
3. The student is not female or a nursing major.  {#3}
4. Are the events "being male" and "being a nursing major" mutually exclusive?  {#4}

1. The person is left-handed or a woman.  {#1}
2. The person is right-handed or a man.  {#2}
3. The person is not right-handed or a man.  {#3}
4. The person is a right-handed woman.  {#4}
5. Are the events "being right-handed" and "being a woman" mutually exclusive?  {#5}

1. The person is frequently or occationaly involved in charity work.  {#1}
2. The person is female or not involved in charity work.  {#2}
3. The person is male or frequently involved in charity work.  {#3}
4. The person is female or not frequently involved in charity work.  {#4}
5. Are the events "being female" and "being frequently involved in charity work" mutually exclusive?  {#5}

1. The person wears contacts or glasses.  {#1}
2. The person is male or wears both contacts and glasses.  {#2}
3. The person is female or wears neither contacts or glasses.  {#3}
4. The person is male or does not wear glasses.  {#4}
5. Are the events "wearing contacts" and "wearing both contacts and glasses" mutually exclusive?  {#5}