Focus Set 3 – Fundamental Counting Principle
Provide answers to # 1 – 10 below.
Show how you set up your problem and then do the math.
1. If there are four roads from town A to town B and three roads from town B to town C, how many routes are there from town A to town C which go through town B?
Number of routes from A to C
= Number of routes from A to B x Number of routes from B to C
= 4 x 3
2. How many different 4-letter radio station call codes are possible if each code must begin with K or W and no letter can be repeated? Examples: WABC, KABC, or WABK
Number of call codes possible
= Product of number of choice of each digit
= 2 x 25 x 24 x 23
3. A firm wants to assign its employees ID numbers that have say x digits each. If a firm has 800 employees, what is the smallest number of digits (that is, the smallest x) that the firm can use for each ID number? Assume that repetition of digits is permitted.
(Hint: There is no formula for this – you just have to reason it out, but you must be enough ID’s to go around!)
For x number of digits, number of distinct ID = 10x
For x =2, number of distinct ID = 100 < 800 For x =3, number of distinct ID = 1000 > 800
Therefore the smallest x is 3
4. In how many ways can 10 questions on a True-False test be answered?
Number of ways
5. In how many ways can a president and vice president be selected from a club consisting of 12 people?
(Assume that these 2 positions cannot be occupied by the same person.)
Number of ways
= Product of number of choice for each position
= 12 x 11
6. In how many ways can 5 people be seated in a row?
Number of ways for 5 people to sit in a row
= 5 x 4 x 3 x 2 x 1
7. How many ways can 6 people be seated in a row, if Ruth must be seated in the first chair?
Since Ruth must sit in first chair, there are on one choice for first chair
Number of ways for remaining 5 people to sit in a row
= 5 x 4 x 3 x 2 x 1
Total number of ways
= 1 x 120
8. How many distinct ordered arrangements can be made with the letters of the word TENNESSEE?
There are 4 repeated E, two repeated N, two repeated S, and totally 9 characters
Number of ways
9. You are trying to schedule classes for next semester and wish to enroll in Math, English, Fine Arts, and History. You have found 4 Math sections, 5 English sections, 6 Fine Arts sections, and 2 History sections that do not have conflicts.
How many different possible schedules can you develop using these options?
There are totally 4 + 5 + 6 + 2 = 17 sections
Number of ways
10. It is lunchtime and you wish to build a pizza with 1 choice of crust, 1 meat, 1 vegetable.
You have the following choices: 2 types of crust, 4 types of meats, and 7 types of vegetables
How many different ways can you build your pizza?
Number of ways to build pizza
= Number of choice of crust x number of choice of meat x number of choice of vegetable
= 2 x 4 x 7
Sustainability is the only way that continuous development and exploitation of resources can be guaranteed. For this reason, there is need for the relevant authorities to ensure that all the players adopt sustainable operations in order to secure the future. This research paper examines the issue of sustainability in Brazil. The paper looks at the issues surrounding sustainability. These issues include profitability, environmental protection as well as lack of proper legal mechanism to control the environmental degradation. Finally, he paper gives recommendations of what can be done to promote sustainable operations by companies.
The urge to meet the current needs is pushing countries and industries to exploit the available resources in ways that are not sustainable. Industries dealing in extraction as well as manufacturing are known to engage in practices that are not sustainable. These practices compromise the availability of these resources to the future generations. The same practices as well may impact negatively on the environment leading to adverse consequences whose effects can be felt by many generations to come. Countries that enjoy vast natural resources are at great risk of engaging in unsustainable practices due to the fact that the vastness of the resources may mislead people to think that they cannot be exhausted. Brazil is of such countries that are endowed with vast natural resources. As a result, industries that deal with exploitation of these resources have for a long time not been very keen in ensuring that their operations are sustainable. The result is environmental degradation that has threatened the well being of the environment.
Brazil is among the few countries in the world that have vast resources. Starting with land, Brazil as a country is very large. It is the largest country in South America both in terms of land area as well as population. Second, Brazil has the largest share of the Amazon rain forest. For many years, Brazil has been rated as the country with the highest rate of deforestation in the world. The effects of deforestation are beginning to be felt in some areas (Caviglia, 2009). Areas that have never experienced flooding are now coping with this problem because there are no trees to control the rate of infiltration. The result is that there is a lot of surface runoff which is the main cause of flooding. Apart from causing flooding, deforestation has many other environmental impacts such as accelerating global warming.
The booming Brazilian economy has made the country to be more ambitious in its economic growth. For example, in 2012, Brazil was working towards overtaking UK in terms of GDP. Although this was possible, it was a very ambitious move given the fact that UK is a strong economy that has been developed over many years. It was therefore a hard task for a relatively young economy such as Brazil to compete with UK. The overambitious development plans have come at a cost to the environment. Industries have tried to make the most out of the environment while at the same time minimizing their cost of production. Although this has come with many economic benefits such as increased employment and better standards of living, the environment has been affected negatively. The increased production means that there are a lot of waste products being generated by these industries. Some of these industries are not able to deal with the increased wastes from these industries and the effect is poor disposal of waste products. Pollution is therefore a big problem in Brazil where land as well as water bodies have been affected. This affects the lives of all the organisms that live on land as well as those found in the water bodies. The polluted water is also a health hazard to the users as their health can be affected by drinking the polluted water.
Sustainability Issues in Brazil
There are a number of issued that are of a major concern when it comes to the sustainability in Brazil. These issues are interrelated and there is a direct relationship between then such that when one is affected it also affects the other. The following are some of the sustainability issues experienced in Brazil.
The main goal of any business enterprise is to make as much profit as possible while at the same time reducing the cost of production to as low as possible. This approach to business affects the ability of a company to invest in activities that do not have an immediate benefit to the business. For this reason, activities that are aimed at conserving the environment are neglected as companies view them as unnecessary costs that can be avoided and which the company can do without. Furthermore, the ever increasing competition in many industries is forcing market players to look for ways of producing their products cost effectively Cavalcanti, 2000). The reasoning behind this is that when a company invests in other activities, it will either increase its product prices or lower its profit margin. The most natural thing for companies to do is to increase the prices. However, this move lenders its products to be uncompetitive in the market. There are few investors who will choose an alternative that will make its products to be uncompetitive. The alternative that many opt for is not to invest in activities that either makes their products uncompetitive or that lower their profit margins. As a result, the issue of environmental management and sustainable development is ignored.
Those industries that are known to be more profitable attract more investors. Such industries include extraction industry. The reason why these industries are more profitable is because they require less investment in terms of raw materials. The only cost involve is capital investment and human resource. Unfortunately, these industries are the ones that greatly contribute to environmental degradation. One of the greatest natural resource that Brazil has is the rain forest. The rainforest in Brazil is the largest in the world. Many companies as well as private individuals have been exploiting this resource for a long time. The level of exploitation has been so high that for more than ten years, Brazil has been ranked as the country with the highest rate of deforestation. Many investors are attracted to the business of exploiting this forest because of the low investment cost and high rate of returns as compared to many industries. Logging and lumbering is a lucrative business in Brazil and this attracts many investors.
The question of environmental protection is the main concern when it comes to sustainability. Many issues pertaining to lack of sustainability result due to the unwillingness of the companies to invest part of their earnings to the management of the environment. Most of the natural resources that are exploited are exhaustible and their continuous use means that in future, there will be little or no resource to exploit. There is therefore need for sustainable exploitation of these resources. Apart from compromising the availability of these resources to the future generations, the operations of these companies are also at risk because once these resources gets depleted, these industries will be forced to close down as they will not have any resources to exploit.
Companies that deal with exploitation of natural resources such as forests need to adopt sustainable practices to ensure that the future generation enjoys this resource. By adopting sustainable practices, these companies will as well be securing their future operations in that they will be ensuring that there will be resources available for them in many years to come. This can only be possible if companies are actively involved in enhancing sustainable exploitation of resources (Cavalcanti, 2000). In the last few years, some companies in Brazil have joined hands to address the issue of sustainable development. This group of companies aims at exploring ways through which their operations depends and also impacts on the environment. The group is made up of eight companies which have accepted to align their operations so that they are consistent with the environmental sustainability.
Walmart is one of the companies in this group. The main concern of Walmart is the increasing trend of ranchers to clear the rain forest in order to pave way for ranches. It is estimated that more than 70 percent of all land that is cleared is used for ranching. The beef production line of this company has developed a plan to discourage ranchers from clearing the forest for ranching. Under this plan, the company anticipates that by 2015, it will not by beef from ranches that sits on the cleared rain forest. This move will discourage the ranchers from clearing the forest for keeping their animals.
Another Brazilian company that is actively involved in ensuring sustainable development is Andre Maggie Group. This is a company that deals with production of agricultural products especially soy. The operations of this company require a lot of wood energy. For a long time, this company depended on wood fuel from the rain forest (Petarnella, 2011). In this way, the company was directly contributing to the destruction of the forest. It was after the realization that its activities of using wood fuel from the forest would in future be detrimental to its activities. Destroying forests can change the micro-climate of the affected region leading to reduced rainfall. Reduced rainfall will consequently affect the growing of soy and the overall production and profitability will decrease. To counter this problem, the company started a project of producing its own wood fuel in a sustainable way.
Lack of Regulatory Legal Structures
The problem of unsustainable development has been fuelled by the lack of a legal framework that regulates the operations of industries. The absence of laws makes the company to engage in activities that compromises the well being of the environment (Otsuki, 2013). In countries that have managed to address the problem of unsustainable development, strict laws have been formulated and those who flout these laws are severely punished. These laws are based on the realization that it is the government that usually carries out remedial measures once the environment has been destroyed. For example, in many countries where deforestation is a major problem, laws have been formulated to ensure that those who cut trees plant others to replace the ones that have been felled. Those players who fail to follow these laws are punished severely by heavy fines being imposed on them or their operating licenses being withdrawn. This ensures sustainability and environmental protection.
The lure of making more profits has blinded companies from seeing the impacts that their operations have on the environment. Investors are not willing to invest in any activity that compromises on its profitability. In Brazil, companies are exploiting the vast resources without much care of the future generations. This has led to the destruction of rain forest through unsustainable felling of trees. When trees are felled in great numbers, the environment is affected negatively in that the micro-climate of the area may be affected leading to change in the weather patterns. This can be a threat especially to agriculture since the change results in reduced rainfall. Pollution is as well a threat to human and animal life in that harmful chemicals are introduced in the environment and these chemicals can pose a health danger once they are ingested in the body. It is apparent that these companies cannot be able to adopt sustainable practices due to the costs involved. This therefore calls for the government to put in place laws that will regulate the operations of all the companies whose operations either directly or indirectly impacts on the environment.
To overcome the problem of environmental degradation and promote sustainable development, a number of measures can be taken to control the operations of all the companies that are involved in the exploitation of natural resources. The government is the agency that should formulate and ensure that the laws are followed by all the players. The first law should aim at compelling companies to take responsibility of their actions. If the company impacts negatively on the environment, it should be compelled to carry out remedial measures so as to protect the environment. The second law should aim at ensuring that all the operations of the company are sustainable. For example, a law can be formulated to ensure that all the companies that are involved in tree harvesting engage in afforestation activities. Once the trees are planted, it will be possible for continuous exploitation since such trees will be harvested in the future.