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In how many different ways can a teacher arrange 6 students in a row of seats?
6! = 6 factorial = 1x2x3x4x5x6 = 720
How does a circular permutation differ from a linear permutation?
For some information, see this link What is circular permutation It goes to another wiki answers article that I just got done writing, and it is both a description of circular permutations and an explanation of how to compute them. I am going to make the assumption that you already know what permutations are in general, otherwise you wouldn't be asking for the differences between the two. Permutations are just ordered arrangements of a set or of a subset of elements. Take the set {a,b,c} We can order the elements to form new ordered sets {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a} For a total of six unique orders, or permutations. Notice that these have a starting point and an ending point... the elements are written in an order, yes, but from left to right in a line. Suppose that there is no start or end, and the right-end wraps around back to the left-beginning in a closed loop, or circle. {a,b,c} is the same as {b,c,a} and {c,a,b}. Element 'a' is followed by 'b', which is followed by 'c'... and 'c', if we are in a circle, is followed by 'a'. This order or pattern is true and the same for each of these three permutations. This makes them ONE circular permutation. In fact, there are only two unique circular permutations for the set {a,b,c}. And those are: {a,b,c} {a,c,b} That is the difference. Here is a real world example... Suppose five people are to sit in a row at the movie theatre. Each seat is unique, there are two ends and each seat has a specific position therein, with no regard to who sits where. This is a linear permutation. There are 5! = 120 unique permutations. Suppose five people are to sit at a round dinner table. The main course is nearest to one seat (a reference point). These five people can sit at the dinner table in 5! = 120 unique permutations. Why? Because each seat is unique. The seats themselves are as unique as the people who are sitting. There is a reference point (the main course) and all seats have a relation to it. It is not unlike numbering the seats themselves. Suppose five people are to sit at a round empty table. Here, any one seat is as good as the next. There is no reference, each seat is non-unique. It doesnt matter where the first person sits. It is his sitting that creates the reference point, and everyone else may sit relative to him. There are 4! = 24 unique seating permutations for these five people.
What fraction of the seats are tier seats?
The answer will depend on WHERE!. In my room, no seats are tier seats.
A small theatre has 30 rows of seats. The first row has 100 seats the second row has 98 seats and the third row has 96 seats. If this pattern continues how many seats will there be in the last row?
42 seats
How many seats fit in 600 square feet?
How big are the seats?
What is circular permutation?
A circular permutation is a type of permutation which has no starting point and no ending point. It is a set of elements that has an order, but no reference point. It circles back around on itself and encloses.For example, think of the number of ways of sitting 5 people around a circular table. If the chairs themselves are ordered then its a regular permutation problem, and is equivalent to sitting in a row at the movie theatre because the seats are as unique as the people who are to be sat. Any object, be it a main course or the hosts seat at a dinner party, or the ends of a row of seats, adds a reference point which makes it a linear permutation problem.If, on the other hand, the chairs are NOT ordered, the table is round, and all the people are unique... its a circular permutation problem because no seat is unique. There is no reference point that is independent of the people sitting. The uniqueness in seating is a result of a persons placement in relation to other people. It is in fact the first person to sit which creates the reference point in which all other sitters sit relative to.Another example. Flags on a flag pole can be arranged like a regular (linear) permutation problem, because it is linear in shape and thus has a top (a reference point). But suppose you have 10 Christmas ornaments to arrange on a reef. If there is a reference point, such as a top to the reef whereby we hang the reef, then it is still a regular permutation problem. The hook is the reference point and all ornaments are placed relative to it.But if the reef has no top or reference, and you can hang the reef any which way you want... then its a circular permutation problem. Once the reef is made it has a fixed ornament order (a circular permutation) but may still be hung differently - depending on how you orientate the reef on the door and where you place the top, it may appear to be a different reef each time. This is because the top reference makes for a different linear permutation for a given circular permutation. Simply put, only so many reefs can be made with 10 Christmas ornaments. If rotating the reef is the only difference between two reefs, then they have the same circular permutation and are in fact the same reef design.That is the basic idea of a circular permutation.Suppose there are n objects and we wish to pick kof them to arrange in a circular permutation. The number of circular permutations are...(k-1)! * nCk =nPk / kAnd is sometimes denoted nP'k with a little prime tack mark above the P.For circular permutations, all elements have to be unique and so without replacement. Unfortunately, I do not know how to solve a circular permutation with replacement problem... nor can I find such references online.Anyway, the basis of the formula is to take a regular permutation and adjust it for the fact that there is no reference point... any arbitrary starting point is just as good as another and does not increase the multiplicity of the pattern. The pattern on whole is what matters, not where it starts. Regular linear permutations count the same circular pattern k times, once for each of the k unique starting places in that pattern.An explanation of the math. The nCkfunction computes the number of ways to choosing, without order, k objects from n unique objects. Of those kunique objects, there are (k-1)! circular permutations. We multiply, as per the fundamental counting principle, to account for all possible orders of all possible combinations of picks. Likewise, nPk is the number of ways of permuting kobjects picked from n unique objects. As explained in the previous paragraph, k objects have the potential for k reference points, and so each circular permutation is counted k times when nPk is computed. Both expressions are algebraically equivalent.If you allow k=n then you are finding the circular permutations of all n-elements of an n-element set, no elements left out. Both expressions simplify into (n-1)!.Then, I suppose, if you need to get why k elements can be arranged in (k-1)! circular permutations in the first place... what relationship between this and the linear permutations of k elements being k! is there? Bare in mind that when the first person of k people sits at a round table, he is creating the reference point. He is arbitrary, but he also turns the circular permutation into a linear permutation. There are k-1 other people to be sat in k-1 other chairs. Voilà, (k-1)! is the number of permutations that exist under these circumstances.Up until now I have talked about what is called Fixed Circular permutations. A reef may not have a top, but it does have a front. This makes it fixed.Now suppose we took something like a bracelet with coloured beads. It is a circular permutation. But you can take that bracelet off of your wrist and turn it around, placing it back on your wrist backwards and so the permutation is now in reverse order. If you are able to do this in your problem, you have what is called Free Circular permutations. Every one unique bracelet, or fixed circular permutation, counts as two: one clockwise and one counter-clockwise. You only need half as many bracelets as there are fixed circular permutations. All you have to do is take the number of fixed circular permutations and divide by two:nP'k / 2
How many seats does a Honda civic wagovan have?
This car has buckets in front, bench in back and seats a total of 5 persons.
What size round table seats eight persons?
10 feet
How did the Virginia Plan arrange for seats to be awarded in the legislature?
Answer:Seats would be awarded to each state by the basis of population.Respond:Thanks!-Wanderingnimph
In how many different ways can a teacher arrange 6 students in a row of seats?
6! = 6 factorial = 1x2x3x4x5x6 = 720
What does the ferris wheel look like?
circular, covered with fancy lights, and rotating on its side, and with seats hollowed out in spheres
How do you change a fuel pump in a 93 Honda?
The fuel pump for a 1993 Honda can be found through the rear seats. Lifting the seats up will reveal a circular panel. When removed the fuel pump can be reached.
What is a circular or ovel shaped building with rows of seats built around a central open space This building was a center for entertainment?
An "amphitheatre" such as the Colosseum
How does a circular permutation differ from a linear permutation?
For some information, see this link What is circular permutation It goes to another wiki answers article that I just got done writing, and it is both a description of circular permutations and an explanation of how to compute them. I am going to make the assumption that you already know what permutations are in general, otherwise you wouldn't be asking for the differences between the two. Permutations are just ordered arrangements of a set or of a subset of elements. Take the set {a,b,c} We can order the elements to form new ordered sets {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a} For a total of six unique orders, or permutations. Notice that these have a starting point and an ending point... the elements are written in an order, yes, but from left to right in a line. Suppose that there is no start or end, and the right-end wraps around back to the left-beginning in a closed loop, or circle. {a,b,c} is the same as {b,c,a} and {c,a,b}. Element 'a' is followed by 'b', which is followed by 'c'... and 'c', if we are in a circle, is followed by 'a'. This order or pattern is true and the same for each of these three permutations. This makes them ONE circular permutation. In fact, there are only two unique circular permutations for the set {a,b,c}. And those are: {a,b,c} {a,c,b} That is the difference. Here is a real world example... Suppose five people are to sit in a row at the movie theatre. Each seat is unique, there are two ends and each seat has a specific position therein, with no regard to who sits where. This is a linear permutation. There are 5! = 120 unique permutations. Suppose five people are to sit at a round dinner table. The main course is nearest to one seat (a reference point). These five people can sit at the dinner table in 5! = 120 unique permutations. Why? Because each seat is unique. The seats themselves are as unique as the people who are sitting. There is a reference point (the main course) and all seats have a relation to it. It is not unlike numbering the seats themselves. Suppose five people are to sit at a round empty table. Here, any one seat is as good as the next. There is no reference, each seat is non-unique. It doesnt matter where the first person sits. It is his sitting that creates the reference point, and everyone else may sit relative to him. There are 4! = 24 unique seating permutations for these five people.
What is some information about Roman theatres?
They were usually (semi) circular with tiered seats (that were more like benches); thus everyone could hear in the theatre.
How were the social classes divided in the theatre in Shakespeare's time?
The social classes in the theatre were arranged so the richer, higher class people had the better veiw and more comfortable seats. As the theatres in shakespeares day were usually circular in shape this meant that the better seats were higher up. The poorer seats were in the open air space in the middle or the theatre with no seats unlike the richer classes above them.
How do plan an auditorium?
To correctly plan an auditorium, make sure that everything is clean including the seats and the entire floor. Arrange seats in a way that leaves room for movement so as to avoid causing commotions in the middle of an event. It is also a good idea to ensure that all seats are placed at a position that allows people to see the center or where the action will be taking place.
