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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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marbles and boxes permutations

In how many ways can five marbles can be dropped in six different boxes? Case (1) marbles are identical Case (2) marbles are distinct. I know this belongs to permutation and I don't know which formula I should adopt
Achari S Ganesha
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Inversion of a permutation

Let's say I have a permutation of $n$ integers defined like this $(a_1, a_2,\ldots,a_n)$. I have also two sets defined like this $A_k = \{ a_i | a_i < a_k, i > k\}$ and $B_i = \{a_k | a_k > a_i, i > k\}$. Clearly, we are talking about inversions,…
user72151
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Find probability that y is divisible by 5 given the following conditions?

y=$x^4$+4 x=any random 5digit natural no.. Find probability that y is divisible by 5? options: a)$1$/$5$ b)$4$/$5$ c)$8$/$9$ MyApproach Total possible outcomes(a)= $8$ . $9$ . $9$ .$9$ . $9$= Total favourable outcomes(b)=$8$ . $9$ . $9$ .$9$ .…
Jack
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How many permutations of $1,...,8$ are a product of a 1-cycle, 2-cycle, 3-cycle?

Any permutation is a product of cycles. For example, the permutation 351642 $(3 \Rightarrow 1, 5 \Rightarrow 2, 1 \Rightarrow 3, 6 \Rightarrow 4, 4 \Rightarrow 5, 2 \Rightarrow 6 )$ can be written as $(31)(2645)$ How many permutations of $1,...,8$…
jeremysanchez50
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How many permutations of the letters ....

D I S C R E T E M A T H E M A T I C S I S R E A L L Y F U N is there such that the words discrete, mathematics, is, really, fun do not appear consecutively. I know that the way to remove repition here is to do the number of possible permutations…
spstephens
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Permutation restricted to subset, reorder the range

Consider the set of numbers $N = \{ 1, \dots, n \}$ and let $S \subseteq N$ be a subset. Now let $\pi : N \rightarrow N$ be bijective, so $\pi$ is a permutation of the numbers from $1$ to $n$. Then $\pi(S) \subset N$ is another subset, and generally…
shuhalo
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Finding rank in a set

I have a set of four numbers. A = {10, 8, 11, 2} I have to find the rank of a number in the above set. Please help me in writing a suitable mathematical equation for finding the rank of a given number. for ex: rank of 8 in the above array is '2'.…
Ram
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Permutation problem, combining objects from multiple sets

I've been working on a hobby coding project in my free time and I've run into quite an interesting problem, which I'm not completely sure how to solve. The problem is roughly stated as follows: There are two sets, set A and set B. Set A contains…
Charles
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Is here any trick for multiplication Sn permutations in this example

I've got problem with permutation group multiplication. Here is an example: Determine the permutation $\alpha = S_9 $ is that $ \alpha*\omega * \alpha^{-1} = \gamma$ . How much of those permutations we have? $ \omega= (13624)(587)(9) $ and $\gamma =…
MatNovice
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5 digit numbers can be selected from the numbers {0,2,4,5,6}

How many different 5 digit numbers can be selected from the numbers {0,2,4,5,6} (Generally 01 and 1 are considered as a one number.) Is the answer 5! ?
isharailanga
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Permutation: $5$ into $8$ if only $2$ can share

I am having trouble figuring out a permutation problem: "In how many ways can $5$ mathematicians be put into $8$ offices, where each mathematician has an office to themselves? What if only $2$ of the mathematicians cannot share an office with…
Newbie
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How many numbers of can by formed by using the digits $1,2,3,4$ and $5$ without repetition which are divisible by $6$?

How many numbers can by formed by using the digits $1,2,3,4$ and $5$ without repetition which are divisible by $6$? My Approach: $3$ digit numbers formed using $1,2,3,4,5$ divisible by $6$ unit digit should be $2/4$ No. can be $XY2$ &…
justin takro
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How many even numbers less than 600 can be made from the digits: 3,3,4,8,9 with each only being used once.

How many even numbers less than 600 can be made from the digits: 3,3,4,8,9 with each only being used once. I can't figure out what to do for the 3rd case where 3 digits are needed
Joe Jewels
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permutation of "counting out"

Josephus problem*: circle=1,2,3,4,5,6,7,8,9,10. count=2. (Beginning at 1) The "last man standing" in this case=9. Order of elimination or permutation (?): 2,4,6,8,10,3,7,1,9 For any size circle and any size count what is the math that produces the…
Ian
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determine whether $ (1 2) H = (1 3 4)$ H without computing cosets

The title kind of says it all: I am suppose to determine whether $(1 2) H = (1 3 4)H$ without computing cosets. Where $G = S_4$ and $H$ is an under group defined by: $H = \{e,(1 2 3 4), (1 3)(2 4), (1 4 3 2),(1 3),(1 4)(2 3),(2 4),(1 2)(3 4)\}$ I…
some_name
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