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- Browse our 9 arrangements of "Show Me the Way."
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How many possible seating arrangements are there?
How many ways can a word be arranged?
How many arrangements are there for the first book?
How many combinations of 3 out of 4 items can be chosen?
Find out how many different ways to choose items. For an in-depth explanation of the formulas please visit Combinations and Permutations.
How many different ways can the letters P, Q, R, S be arranged? The answer is 4! = 24. This is because there are four spaces to be filled: _, _, _, _ The first space can be filled by any one of the four letters. The second space can be filled by any of the remaining 3 letters.
Using our combination calculator, you can calculate that there are 2,598,960 such combinations possible, therefore the chance of drawing a particular hand is 1 / 2,598,960. Here is a more visual example of how combinations work.
About. Transcript. Want to learn about the permutation formula and how to apply it to tricky problems? Explore this useful technique by solving seating arrangement problems with factorial notation and a general formula. This video also demonstrates the benefits of deductive reasoning over memorization. Questions. Tips & Thanks.
- 8 min
- If the number of chairs is indeed greater than the number of people, it breaks the generic formula o...The general permutation can be thought of in two ways: who ends up seated in each chair, or which chair each person chooses to sit in. This is less...
- How many words can be formed using the word Pencil such that N is always next to E?First let's think about it a bit, to figure out how many ways you can arrange "Pencil" with N and E always next to one another it's going to be all...
- Why is the factorial symbol an exclamation mark?The notation (and the name "factorial") was chosen by Christian Kramp, a French mathematician who did much of the early work in combinatorics. He d...
- What if each person could also have an orientation? Say: 1 of 4 possibilities. I can reason that the...The orientation doesn't depend on their seat or anyone else's orientation. So there would be 5! ways of arranging 5 people and for each of those 5...
- At 6:42 he says that the formula is n!/(n-r)!, but in the first example there are 5 seats and 5 peop...It's because 0! = 1 not zero. https://www.khanacademy.org/math/precalculus/prob-comb/combinatorics-precalc/v/zero-factorial-or-0
- Would (n!)/((r-1)!) also work?No. The formula n!/(n-r)! works because n! gives the amount ways to arrange n object over n spaces. But since we are working with r spaces, there w...
- How would you go about finding permutations of a number, where some of the digits repeat? ex. 112233We have 6 digits, and thus a preliminary count of 6!. However, note that several of these 6! configurations are not distinct. In particular, we hav...
- from a group of 9 different books 4 books are to be selected and arrange on a shelf.how many arrange...There are 9 choices for the first book. For each of those choices, there are 8 choices for the second book, for a total of 72. For each of those, t...
There are 5! possible seating arrangements without the condition. From that, we subtract all arrangements where A and B sit next to each other. The easiest way to do that is to count A and B as one person.
- 6 min
- Okay, so this makes sense, but what's a good explanation for why we multiply instead of add, other t...We multiply because these quantities depend on each other. If they are independent of each other we add. Hope this helps!
- So what if there are 5 people and 15 chairs?Switch your frame of reference - choose people for the chairs, and not chairs for the people.
- Can we have factorials for negative numbers?Not typically. There is a generalization of the factorial function called the gamma function, but even this doesn't give values for negative intege...
- What if the number of seats is greater than the number of people or people must sit in a certain sea...Good question. The permutation formula works, but you need to think of it in the right way. In this instance, you can think about how many ways you...
- In this video Sal discuses how people can be arranged around a round table. What if the table was in...If I'm not mistaken, then you can use the same method. I don't think the shape of the table matters. But please don't depend on this answer, I'm ve...
- What about calculating 5.3! (FACTORIAL of decimal ) . .You ask google for that It gives 5.3! = 201.8...The gamma function is given as an integral, which can be approximated by evaluating a certain exponential function at a bunch of points, multiplyin...
- I think a good analogy for this is to think of a branching tree diagram. • / | \ *3 • • • / \ / \ / ...Your analogy of a branching tree diagram to explain the concept of permutations is a good one. The branches of the tree represent the possible choi...
- How many ways can six students be arranged on a bench seat with space for three? I'm stuckWell it works pretty much the same way as the other cases. If you had six students and six seats, it would 6 * 5 * 4 * 3 * 2 * 1 = 6! = 720 But wit...
Mar 10, 2024 · This combination calculator (n choose k calculator) is a tool that helps you not only determine the number of combinations in a set (often denoted as nCr), but it also shows you every single possible combination (or permutation) of your set, up to the length of 20 elements. However, be careful!
Given a list of \( n\) distinct objects, how many different permutations of the objects are there? Since each permutation is an ordering, start with an empty ordering which consists of \( n\) positions in a line to be filled by the \(n\) objects.
