I understand you are taking a college course in mathematics and studying permutations and combinations. Permutations and Combinations date back through the ages. According to Thomas & Pirnot (2014), there is evidence of these mathematical concepts as early as AD 200. As we solve some problems you will see why understanding these concepts is important especially when dealing with large values.
I also understand you are having problems understanding their subtle differences, corresponding formulas nPr and nCr and the fundamental counting principle. Before we review some exercises, I would like to provide you with some definitions you will need in solving some problems.
According to Thomas & Pirnot (2014), a permutation is an ordering of distinct objects in a straight line. If we select r different objects from a set of n objects and arrange them in a straight line, this is called a permutation of n objects taken r at a time. The number of permutations of n objects taken r at a time is denoted by P (n,r).
In working with permutations and combinations we are choosing r different objects from a set of n objects. The big difference is whether the order of the objects is important. If the order of the objects matter, we are dealing with permutations. If the order does not matter, then we are working with combinations (Thomas & Pirnot, (2014), p. 624, 626).
According to Thomas & Pirnot (2014), in combinations if we are choosing r objects from a set of n objects and are not interested in the order of the objects, then to count the number of choices, we must divide P (n,r)* by r!. We now state this formally: Formula for computing C(n,r). If we chose r objects from a set of n objects we say we are forming a combination of n objects ta...
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...someone who is not the owner of the IPad will guess the code?
Solution:
36C4=36x35x34x33=1,413,720
There are 10 numeric digits on a keypad and 26 letters. Adding these we get 36 digits representing the first code, 35 digits are used for the second code, 34 digits are used for the third code and 33 digits for the fourth code. Leaving us with 1,413,720 possible pass code combinations someone other than the owner can use. The likelihood of all these combinations being used is slim.
These counting principles are important in understanding odds. For example, I rarely play the lottery but have relatives who play on a regular basis. Mathematically the odds are slim, however the game can only be won by chance. I hope the definitions and the equations have brought clarity to the subject.
Reference
T. L. Pirnot.. (2014). Mathematics all around. (5th ed.). Boston, MA.
(http://www.encyclopedia.com/doc/1O7-densityfrequencydominance.html) Biodiversity is the number of richness or the number of species in a local area. This happens when someone can look at a species, in order to indicate a degree of uncertainty. This can happen by calculating the number of species given, where the individual is picked at random from the community. In other words, if the diversity is high, then oneself will have a poorer chance of correctly calculating the species of the next individual picked at random. (http://www.tiem.utk.edu/~gross/bioed/bealsmodules/shannonDI.html) This experiment was a way to find out the diversity of the school parking lot and the possibility to identify the type or model of the student’s, faculties and guest
Thus total number of operations needed to execute the function for any given n, can be expressed as sum of 2 operations and the total number of operations needed to execute the function for n-1. Also when n=1, it just needs one operation to execute the function
Within supply and demand theory there are complementary and substitute goods. Complementary goods are related goods used in conjunction with each other, such as hot dogs and hot dog buns or
In their most basic and natural settings, these two concepts can simply be defined as such:
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Before choosing the Electoral College, the Constitutional Convention came up with several methods of selecting a president with those reasons under consider...
First we are going to talk about probability theory, which has to do with mathematics and analysis of random phenomena. You are probably used to putting the number of outcomes over the total amount of the object or total amount what you have. An example is, if you have a normal dice and you want the probability of rolling an odd number, you would take the total amount of odd numbers (3) and put that over the total (6) amount of numbers on the dice like so 3/6 which you can also reduce it to ½ because 3 is half of 6. This theory has been around since the sixteenth century and started off as the outcome you would get in a game, which was created by Pierre de Fermat, Blaise Pascal and Gerolamo Cardano. Later on in the seventeenth century Christiaan Huygens published a book on the subject.
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Plurality is also known as “first past the post,” plurality is by far the most common voting system for single-winner races. Unfortunately your “vote” is the name of a single candidate, and the most named candidate wins.
Understanding the Symbols in The Lottery. Elton Gahr, 5 Jan 2012. Web. The Web.
To investigate the notion of numeracy, I approach seven people to give their view of numeracy and how it relates to mathematics. The following is a discussion of two responses I receive from this short survey. I shall briefly discuss their views of numeracy and how it relates to mathematics in the light of the Australian Curriculum as well as the 21st Century Numeracy Model (Goos 2007). Note: see appendix 1 for their responses.
Probability is always surrounding us from stock markets to the ever-simple heads or tails. This very complicated area of mathematics can be explained in a simpler way. It is how likely an event is to happen. The probability of an event will always be between 0 and 1. The closer it is to one, the more likely the event is to happen.
By using combinations from the above – But this approach has to be made with caution, because confusion can appear in the message.
"A periodic table is an arrangement of elements in which the elements are separated into groups based on a set of repeating properties." Basically it shows us all known elements in the world. For one to read the periodic table he should beware that the atomic number comes first in the square , and referring to the atomic number its the number of protons found in the nucleus of an atom. Following the atomic number is the symbol, which is usually the abbreviation of the element's name. For example Carbon is referred to as " C". Then, the element’s name is shown right after the symbol. Lastly, there's the mass number, which is the number of protons and neutrons in the nucleus of an atom. So simply for us to find the number of protons we automatically
and 8 can be written as 2 , while 5, 6, and 7 can be written using some