- The first time you're exposed to permutations and combinations it takes a little bit to get your brain around it, so I think it never hurts to do as many examples. But each incremental example I'm gonna review what we've done before, but hopefully go a little bit further. So let's just take another example. This is in the same vein.
In videos after this I'll start using other examples, other than just people sitting in chairs, but let's just stick with it for now. Let's say we have six people again. Person A, B, C, D, E, and F, so we have six people.
Now let's put them into four chairs. We can go through this fairly quickly, one, two, three, four chairs. We've seen this show multiple times. How many ways, how many permutations are there of putting these six people into four chairs? Well the first chair, if we seat them in order, we might as well, we can say well there'd be six possibilities here. For each of those six possibilities there would be five possibilities of who we'd put here, because one person's already sitting down Oncasinogames.
For each of these 30 possibilities of seating these first two people, there'd be four possibilities of who we put in chair number three. Then for each of these, what is this, 120 possibilities there would be three possibilities of who we put in chair four. This six times five times four times three is the number of permutations.
We've seen in one of the early videos on permutations that, when we talk about the permutation formula, one way to write this, if we wanted to write in terms of factorial, we could write this as six factorial, six factorial which is going to be equal to six times five times four times three times two times one, but we wanna get rid of the two times one. We're gonna divide that, we're gonna divide that. Now what's two times one? Two times one is two factorial.
Where do we get that? We wanted the first four, the first four factors of six factorial. That's where the four came from.
We wanted the first four factors, so the way we got two is we said six minus four. Six minus four, that's gonna give us the number that we wanna get rid of. We wanted to get rid of two or the factors we wanna get rid of. That's going to give us two factorial. If we do six minus four factorial. That's going to give us two factorial, which is two times one.
Then these cancel out, and we are all set. This is one way, I put in the particular numbers here, but this is a review of the permutations formula, where people say, "Hey, if I'm saying n, "if I'm taking n things, then I want to figure out "how many permutations are there "of putting them into let's say k spots, "it's going to be equal to n factorial "over n minus k factorial." That's exactly what we did over here, where six is n and k, or four is k. Four is k. Actually let me color code the whole thing so that we see the parallel. All of that is review.
Then we went into the world of combinations. In the world of combinations, we said permutations make a difference between who's sitting in what chair. For example, in the permutations world, and this is all review, we've covered this in the combinations video, in the permutations world A, B, C, D, and D, A, B, C, these would be two different permutations that's being counted in whatever number this is. This is what? This is 30 times twelve.
This is equal to 360. Each of these, this is one permutation, this is another permutation, and if we keep doing it we would count up to 360. But we learned in combinations, when we're thinking about combinations, let me write combinations. If we're saying n choose, n choose k, or how many combinations are there?
If we take k things, and we just wanna figure out how many combinatio- If we start with n, if we have pool of n things, and we wanna say how many combinations of k things are there, then we would count these as the same combination. What we really wanna do is we wanna take the number of permutations there are. We wanna take the number of permutations there are, which is equal to n factorial over n minus k factorial, over n minus k factorial, and we wanna divide by the number of ways that you can arrange four people. Once again, this takes- I remember the first time I learned it took my brain a little while. If it's taking you a little while to think about it, not a big deal.
It can be confusing at first, but hopefully if you keep thinking about it hopefully you will see clarity at some moment. What we wanna do is we wanna divide by all of the ways that you can arrange four things. Cuz once again, in the permutations it's counting all of the different arrangements of four things, but we don't wanna count all of those different arrangements of four things. We wanna just say they're all one combination. We wanna divide by the number of ways to arrange four things. Or the number of ways to arrange k things.
Let me write this down. What is the number of ways, number of ways, to arrange k things, k things, in k spots. I encourage you to pause the video, because this actually a review from the first permutation video. If you have k spots, let me do it so if this is the first spot, the second spot, third spot, and then you're gonna go all the way to the kth spot. For the first spot there could be k possibilities. There's k things that could take the first spot.
For each of those k possibilities, how many things can be in the second spot? It's gonna be k minus one, because you already put, you already put something in the first spot. Then over here, what's it gonna be? K minus two all the way to the last spot, there's only one thing that can be put in the last spot. What is this thing here?
K times k minus one times k minus two times k minus three all the way down to one. This is just equal to k factorial. The number of ways to arrange k things in k spots, k factorial. The number of ways to arrange four things in four spots, that's four factorial. The number of ways to arrange three things in three spots, it's three factorial.
We could just divide this. We could just divide this by k factorial. This would get us, this would get us, n factorial divided by k factorial, k factorial times, times n minus k factorial, n minus k, n minus k, I'll put the factorial right over there. This right over here is the formula. This right over here is the formula for combinations. Sometimes this is also called the binomial coefficient.
People always call this n choose k. They'll also write it like this, n choose k, especially when they're thinking in terms of binomial coefficients. I got into kind of an abstract tangent here, when I started getting into the general formula. Let's go back to our example. In our example we saw that there was 360 ways of seating six people into four chairs. What if we didn't care about who's sitting in which chairs and just wanna say, "How many ways are there "to choose four people "from a pool of six?"
That would be that would be how many ways are there. That would be six. How many combinations if I'm starting with a pool of six, how many combinations are there? How many combinations are there for selecting four? Another way of thinking about it is how many ways are there to, from a pool of six items, people in this example, how many ways are there to choose four of them. That is going to be, we could do it- I'll apply the formula first, and then I'll reason through it.
And like I always say, I'm not a huge fan of the formula. Every time I revisit it after a few years, actually just rethink about it, as opposed to memorizing it, because memorizing is a good way to not understand what's actually going on, but if we just apply the formula here, I really want you to understand what's happening in the formula, it would be six factorial over four factorial, over four factorial, times six minus four factorial, six, oops let me just, This is six minus four factorial, so this part right over here, six minus four fa- Let me write it out because I know this can be a little bit confusing the first time you see it. So six minus four factorial, factorial, which is equal to, which is equal to six factorial over four factorial, over four factorial, times this thing right over here is two factorial, times two factorial, which is going to be equal to, we can just write out the factorials, six times five times four times three times two times one, over four. Four time three times two times one times, times two times one.
Of course that's going to cancel with that. Then the one doesn't really change the value, so let me get rid of this one here. Let's see, this three can cancel with this three. This four could cancel with this four. Then it's six divided by two is going to be three. So we are just left with three times five.
We are left with, we are left with, there's fifteen combinations. There's 360 permutations for putting six people into four chairs, but there's only 15 combinations, because we're no longer counting all of the different arrangements for the same four people in the four chairs. We're saying, "Hey if it's the same four people, "that is now one combination." You can see how many ways are there to arrange four people into four chairs?
That's the four factorial part right over here. The four factorial part right over here, which is four times three times two times one, which is 24. We essentially just took the 360 divided by 24 to get 15. Once again, I don't think I can stress this enough. I wanna make it clear where this is coming from. This right over here, let me circle, this piece right over here is the number of permutations.
This is really just so you can get to six times five times four times three, which is exactly what we did up here, where we reasoned through it. Then we just wanna divide by the number of ways you can arrange four items in four spaces.
One thing I loved about being a university student was the amount of holiday time – three or four months over summer as standard, which is something you’ll never have again until you retire, not even if you choose to become a teacher for those 6-week summer holidays.
While it’s nice to chill out and laze around the house for a while, it can soon grow tiresome and you might start musing about how you can fill this time with something useful and fun.
Here are a few ideas of things you can do during university holiday time that are both interesting and really valuable for your future career…
There is a UK company called Traveleyes which puts together holiday packages for people with visual impairments. They also offer holidays to sighted people at substantially reduced rates; in turn for your discounted holiday, you volunteer to help your fellow holiday makers who have visual impairments. This involves guiding and also describing the various places that you visit.
Volunteering on a project such as this is a great way to have fun while getting valuable experience for your CV – it will give you something really interesting and different to talk about at job interviews. It’s also an affordable way to travel abroad! Although the company is UK based, it is available to people outside the UK.
There is also a company called Original Volunteers, which deals in more traditional volunteering opportunities abroad for as little as £35 a week, including accommodation.
Knowledge is power
The idea of doing more reading and learning in holiday time may sound a bit arduous, but there are lots of options for you to do some additional learning that you can do at your own pace, online and often for free. And of course, if it’s something you’re interested in then you are likely to find it enjoyable.
There are lots of online learning resources that offer free courses, such as Open Culture which offers approximately 700 free online arts and sciences courses. The BBC learning website also features a number of free online courses including languages, English, maths, science, first-aid, food and catering, media studies, gardening, health, history, and IT.
There are also certain skills that are considered specialist likes sales and marketing, but are so valuable that they can really be considered as key skills. The holiday time gives you an excellent opportunity to obtain and hone these skills to impress future employers.
If you’re an aspiring writer, artist or consultant, one thing that you will almost certainly want is your own website. You’ll also want people to be able to easily find you. You can of course pay someone to sort all this out for you, but you can save money and get ahead by learning the skills needed to do it yourself.
Let us know how you’ve spent your university holidays. Have you any good suggestions, or have you tried the above ideas? Leave a comment below.
People all over the world are learning how to deal with job loss they did not see coming. It can be disheartening to find yourself suddenly unemployed especially if you were a good worker for a number of years. However, it is important to keep a positive attitude in order to turn things around for yourself.
Many people become depressed when they lose their job which is the direct result of constantly thinking negatively about the situation. But every dark cloud has a silver lining. A job loss could be just the opportunity you needed to move your life in different direction.
It is easy to get comfortable in a job that brings very little joy but which provides a steady paycheck. Sometimes it takes something drastic, such as an unexpected unemployment, to put us on the path towards a more fulfilling life. Take some time to explore the possibilities.
Since losing a job can be a tremendous jolt to the system, spend a few days recovering from the shock. Then plan what you will do next and take the steps necessary to turn your ideas into reality. If you want to find new employment then rewrite your resume and start talking to people about job opportunities. If you would rather become self-employed, look at different ways you can start your own business.
There are a number of resources that can help you get back on your feet so take full advantage of them. Even though you may not think you’ll qualify, apply for unemployment benefits. You should also avail yourself of the help of job counselors. Generally, they will know of other programs that assist you in turning your luck around.
Learning how to deal job loss can be a painful event. However, if you keep your head up and move in the direction of your goals you will come through the challenge better and stronger than ever.
A career as a dental assistant will unlock lots of doors of opportunity.
Dental assistants will be among the fastest growing occupations from now until 2012. This is because people are starting to become more interested in their oral health. Technological advances have led numerous people to the dentist’s agency for cosmetic dental procedures instead of merely cleanings and major dental work. Furthermore, people are living longer, thus their teeth need more care to stay healthy all the way through their lives.
The most common place to find jobs for dental assistants is in a dental agency.
Here they offer a diversity of services. They regularly help out to comfort scared patients prior to procedures and give follow-up care at the end of appointment. Dental assistants clean the tools used and ensure that each work unit has the tools and equipment lay out for the next patient’s procedures.
Dental assistants in the dental office work very closely with dentists and hygienists.
They often sit in on all procedures, handing staff the necessary tools. Dentist agencies are in general small so dental assistants often aid with lab work. This includes making molds of teeth for caps, bridges, and other dental work. They may also be required to assist with the taking of X-rays.
A common place for dental assistants to be employed is in prisons. With more and more prisons being built across the country, dental assistants are in high demand for federal, state and private prisons.
Working as a dental assistant in a prison environment requires more carefulness than at a conventional dental agency.
All nursing assistants ought to be aware of the risk of contagious diseases that are transmitted through saliva and blood. The rate of these diseases, especially HIV, is much greater with a prison population than with the general community. Furthermore, a few prisoners might attempt to assault by biting.
Nursing assistants in a prison setting need to be alert, and in no way let down their guard.
Prisoners regularly seek out every opportunity to breakout or to obtain weapons. They can make use of a dental tool as a weapon against you, other staff or other prisoner. It is incredibly critical that you keep very close track of all dental instruments in a prison location. By no means leave a tool available to a prisoner for a minute. If you discover a tool is gone, warn your supervisor and follow the procedures in the prison policy.
For those dental assistants wanting to help the lower income populations, securing employment in a Child Development Center, Head Start or migrant program is a great way to give back to the public. Often, these people can not find the money for dental care and go without it if the services are not presented as part of a government program. Employment in these types of agencies as a dental assistant often pays less than other employment opportunities in the field. However, numerous dental assistants choose to help the poor instead of earning more funds.
There are a lot of opportunities to work as a dental assistant for agencies that serve individuals with disabilities.
Often, dental assistants are scared of working with this population. In spite of this, when you feel comfortable with people with disabilities, you will be able to offer suitable care to people in need, regardless of their mental or physical appearance.
A career as a dental assistant offers various areas of employment, including the dental clinics, prisons, low-income programs, and facilities that serve people with disabilities.
The ability to select the type of environment you want to use your dental assistant skills in makes the field even more attractive. If you are unsure whether a specific type of agency is a good option for you, talk with them. Ask if you can shadow another dental assistant who works there for a longer time. This should give you enough exposure to activities that take place in that agency.
With health and wellness being of utmost importance to people today, many health and medical-related industries need more professionals and staff, and one such job is that of the pharmacy technician. There are several pharmacy technician jobs being offered almost anywhere in the country.
Pharmacy technicians normally provide medication and a variety of products to patients, usually in hospitals, clinics or even in some drug stores.
They work with pharmacists and doctors as they are assigned with tasks that deal with preparation of prescribed medicines given to patients and sometimes, they could also be involved with the preparation or compounding of medications.
In addition, they too can virtually do anything else that would assist the doctor or pharmacist that they are working with, oftentimes acting as some kind of gatekeepers or secretaries who make calls, maintain prescription inventories, coordinate activities of pharmacy clerks, process expenses and orders and help out with the management. Although pharmacy technicians do not counsel patients on their medications, most pharmacy technician jobs require them to establish and maintain cooperative relationships with patients, responding quickly and responsibly to their needs and helping them solve their problems.
If you are looking for pharmacy technician jobs, you need a nurse resume, prepared by Craftresumes writers. Then you can expect that among the requirements would include being a high school graduate, and being able to complete some kind of pharmacy technician training program, and at times even having a pharmacy technician license for the specific state which you want to work for. What’s important of course is that you are able to perform various procedures in connection to providing pharmacy services, like filling out forms for customers and patients appropriately, knowing abbreviations and terminologies related to medicine and pharmacy, having a reasonable set of skills in using computers (since you may be asked to input or encode information) and also processes that involve the preparation, dispensation and distribution of medications under the supervision of a pharmacist. Customer services skills are found to be very helpful in this kind of job as well.
The job might entail shifting or regular schedules, depending on the employer. You may also be paid by the hour, especially if you’re having it as a part-time job. Some good companies also offer competitive compensation packages which include insurance, paid time off, pension, paid holidays and many others.
From identifying and also handling deadly illness, decreasing accident dangers to uncovering monetary fraudulence, Google claimed that it intended to improve the lifestyle by decreasing entrance barriers to making use of these innovations. These modern technologies would certainly also add a great deal of value to self-driving vehicles, Google Photos' search abilities or even Snapchat filters that transform the images of customers into computer animated images.
" Google's cloud platform already delivers client applications to over a billion customers each day," stated Fei-Fei Li, primary scientist of AI as well as machine learning at Google Cloud. "Now if you could just imagine, integrating the enormous reach of this system with the power of AI and also making it offered to everybody."
AI intends to construct machines that could replicate human knowledge procedures, while Stanford University explains machine learning as "the science of obtaining computers to act without being explicitly programmed."
"Now finally we are beginning to beam the light on the dark matter of the digital world," claimed Ms. Li, that is likewise the supervisor of the Artificial Intelligence as well as Vision Labs at Stanford College.
Robert is a blogger at Craftresumes, novelist and passionate reader. He is a hiking addict, vegan, hiphop head, reclaimed wood collector and proud pixelpusher. Producing at the nexus of art and programing to save the world from bad design. He sometimes makes random things with friends.