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Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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Maximum number of points of intersection

The greatest number of points of intersection of 8 straight lines and 4 circles are? My attempt:Assuming every line cuts all the four circles at two points each, the points of intersection of lines with circles=64. Now, each circle cuts the other 3…
GrandAlpha
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permutations repetitions/no repetitions

License plates consist of sequence of 3 letters followed by 3 digits. How can they be arranged if (i) no repetition of letters is permitted, how many possible license plates are there? should it be $26P3 \cdot (10^3)$ or $3! \cdot (10^3)$?
Hamza750
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Permutation Game problem

could you help me to understand this problem? This is the problem statement Alice and Bob are playing a game called "The Permutation Game". The game is parameterized with the int N. At the start of the game, Alice chooses a positive integer x, and…
user2487467
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Permutations with repeating digits

My question is this : how many distinct two digit numbers can be produced from numbers $4, 3, 3, 1$? When applying the formula $$\frac{4!}{(4-2)!2!}$$ you come up with $6$, yet when doing the problem manually, I come up with $7$ numbers, namely $41,…
Mathkin
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Group Theory - Permutations

If $B \in S_7$ and $|B^3| = 7$, prove that $|B|=7$. Solution: As $o(B^k) = o(B) / (o(B),k) $ Thus $|B| / (|B|,3) = 7$ Let $|B| = 7a$. Then $7a/(7a,3)$ should be $7a/a = 7$ or $(7a,3) = a$. As $3$ is a prime number and can only be factored into $3$…
George J. Adams
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Proof of 2^n deck of card, it will be reverse order performing n perfect in-shuffle.

I am now trying to prove performing n perfect in-shuffle with 2^n deck of card, and then it will be resulting reverse order. For example, Initial : [1, 2, 3, 4] 1st round : [3, 1, 4, 2] 2nd round : [4, 3, 2, 1] = reverse order! Until now, I…
Tony_SSU
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How do I calculate the number of permutations of the list $(6, 6 ,5, 4)$?

I have the list $l = (6, 6, 5, 4)$ and want to how to calculate the possible number of permutations. By using brute force I know that there are 12 possible permutations: $$\{(6, 5, 6, 4), (6, 6, 5, 4), (5, 6, 6, 4), (6, 4, 5, 6), (6, 5, 4, 6), …
bodokaiser
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How many way can 3 distinct letter and 2 distinct digit be arranged if the digit must be together

Hi mind helping me out for this question ? How many way can 3 distinct letter and 2 distinct digit be arranged if the digit must be together. Thanks.
user213471
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permutations of objects containing non distiguishable objects in sample

if we have 3 types of objects A,B,C . If I want to make permutation without repeat n! = 3! = 6 but if i will take r sample so n!/(n-r)! if I want to make arrangment of undistinguishable Objects like 2A 2B 2C so I may use n!/A!B!C! how to make…
youssef
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Permutation question, 9 seats.. 3 nationalities.

There are 9 seats in a row, 3 Chinese people.. 3 Russians and 3 Poles. How many ways are there for those people to be seated, so that they don't sit next to a person of the same nationality. Would anyone be so kind, so as to tell me if this is the…
user211302
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How many ways can 5 students be seated in a row of 6 chairs if 2 students must sit togegher?

The 2 adjacent students will have an arrangement of 5. Next, the open 4 chairs can be filled by either of the 3 students for 3!= 6. The product of 5 and 6 = 30. Am I taking the proper approach?
Jay Hicks
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Is it a Permutation or Combinatorics?

I'm a programmer and I need to write an algebraic notation for a LOOP made in one of our programs. I don't have Mathematica software, but just MathType to write formulas and notations. The program executes 2 kinds of operation with bytes and bits…
David BS
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Simplifying Permutations

Could someone explain the process of simplifying the following permutation in $S_6$ (1,3,5)(2,4,5)(2,3,6) An explanation on how you arrived at the simplified form would also be greatly appreciated. Thanks
Caitlin Y
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Word Permutations

How many words can we build using exactly 5 A's, 5 B's and 5 C's if the first 5 letters cannot be A's, the second 5 letters cannot be B's and the third 5 letters cannot be C's? Can anyone help me? I have been trying many ways of doing this, all to…
user197879
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Unique calendars

We have to make $3000$ unique calendars. There are unique in the sense that each calendar will have twelve designs (one for each month) in such a sequence that no two calendars are exactly identical. Our intention is to create $x$ number of designs…
Confused
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