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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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PERMUTATIONS Olympiad Number Theory Question

AIMO 2020 Olympiad Permutation Questionenter image description here This question was encountered during a mathematics competition, and I thought that Induction on k would be a suitable method of solving it. Am I right?
Qing Zhu
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How do you solve for number of variations for a specific number of repetitions?

I am trying to determine how many different permutations I can make with 4 values {1,2,3,4} for an 8 chain sequence. Normally, I would simply do 4 to the power of 8. However, there can only be two repetitions of each value -- so 11223344 is a…
Zofia Korsak
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How many ternary (0, 1, 2) sequences of length 10 are there without any pair of consecutive digits the same? Need help understanding.

My work: $3$ (as there are $3$ choices for first digit) x $2^9$ (only $2$ digits as choices to avoid consecutive digits from then on) x $10$ (permutations where we move the 3 around) = 15360 sequences But other people are saying that the answer is…
user827508
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set theory ,permutation and combination.

Let P be the set of k elements.What is the number of ways we can choose an ordered pair (R,S).Where R and S are disjoint subsets of P.
mmittal1971
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Find the smallest positive integer k such that $p^k = 1A$

Given: $$p = \begin{bmatrix} 1 &2 &3 &4 &5 &6 &7 &8 &9 \\ 1&5 &7 &4 &6 &9 &3 &2 &8 \end{bmatrix}$$ How would I go about determining $k$ such that: $$p^k = \begin{bmatrix} 1 &2 &3 &4 &5 &6 &7 &8 &9 \\ 1&2 &3 &4 &5 &6 &7…
Damian Jacobs
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How do I make a function where the range of the function is a permutation of the given function domain?

An example for 0, 1, 2, 3, 4, 5 would be: f(0)=5; f(1)=1; f(2)=0; f(3)=4; f(4)=2; f(5)=3; I have found f(x) = 911 * x % N to work where 911 can be any large prime number, but I noticed patterns in the list of numbers resulted. In a line chart with…
Discipol
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Doubt: no. of rectangles in chess board

My text book had a question to find the no. of rectangles in a chessboard. My attempt was that out of $64$ points if we choose any $4$ points, a rectangle is formed and hence no. of rectangles in $C(64,4)$ [$64$ choose $4$]. But in the book its…
BrainNuke
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Given an integer $n$, is there a derangement of $n$ items such that repeating it $n!$ times will reach all possible permutations?

Suppose you have a sequence, \$S\$, of \$n\$ items and you want to enumerate all possible permutations of those items. Consider the transformation $$ S^{\prime} = ( S_{a_1}, S_{a_2} ... S_{a_n} ) $$ Is there a transformation (specifically, a…
Beefster
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What is the permutation of choosing the just 3 balls in a pool of 16 balls?

I was reading permutation without repetition which says that In a pool if $16$ balls there are $N!$ possibilities, which is, $16 × 15 × 14 × 13 × ... = 20922789888000$ possibilities But when we don't want to choose them all, just $3$ of them, and…
mahesh87
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Plausible gene sequences

I'm not looking for a specific answer to a question (below). I think it is likely that the 'kind' of problem I have has been studied (and has a name ;). But I don't know what that might be. So I'm mostly looking for a name or a pointer in the…
TimG
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Permutation problem regarding arranging certain people in a line without succession

The problem: Find the number of ways in which 14 high-school juniors and 10 high-school seniors can be arranged in a line so that no two high-school seniors may occupy consecutive positions My solution: I will try find all the permutations where…
tryingtobeastoic
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Permutation Problem involving repetitions in the number of things to be chosen from and the number of slots being unequal to the number of things

Problem: A person has one white, two red, and three green flags. How many different signals can they make, each containing four flags arranged one above the other? My attempt: We have 4 slots and 6 things to choose from. But among the 6 things,…
tryingtobeastoic
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probability, women selected, brewery selected

There are $9$ women, who each own $4$ breweries, and $12$ men, who each own $9$ breweries. I pick $4$ people at random (without replacing). a) Let $Y$ = the total number of breweries. Write down the pmf of $Y$ (probability of each possible number of…
rgentil32
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How to count all possible convertions to limited string size?

I have a string 1111 and I know that 1 can be converted to 1, 10 or 100 but the string will be still 4 symbols length, so actually each 0 sign replaces next symbol. So it could be 1111 1110 1101 1011 1010 1001 1100 How to count all possible…
user3360601
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Permutations of two groups of people

When question is "What is the number of ways to create a group of 5 from 17 girls and 20 boys when you have to select at least 3 girls I needs a simple explanation why it is that $$ {17\choose3} {20\choose2} + {17\choose 4} {20 \choose 1} + {17…
Shaun Vermaak
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