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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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how to calculate permutations when two dice are rolled

I am trying to understand what permutations mean, so I am taking two 6 sided dice and rolling, the total permutations are 36 - this is something that I understand (1,1), (1,2), (1,3), (1,4), (1,5), (1,6) (2,1), (2,2), (2,3), (2,4), (2,5),…
hp 5g
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Count of permutation for empty set, why is it 1, not 0?

Count of permutation of n different items are: A(n) = 1*2* .. *n e.g: [1] -> {1} // 1 [1,2] -> {1,2}, {2,1} // 2 [1,2,3] -> {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1} // 6 So what is the permutation of: [], (aka. empty input). I've…
Eric
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Minimal order of a set of permutations

We say that the order of a permutation $\sigma$ is the smallest integer $k$ such that $\sigma^k$ is the identity permutation. That is, we repeatedly apply $\sigma$ until we get the identity permutation. Suppose I have a set $S$ of permutations, all…
orlp
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How many permutation of 6 elements that can each be oriented in 2 ways?

I've trying to find the answer to this but failing. I understand that if the order matters, there are 6! permutations of 6 elements, or 720. But I'm trying to figure out how many permutations there are if each of the six elements is oriented in one…
Jmb1978
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calculate permutations of a 32 bit word (Marching 1's)

I am not mathematically proficient so please keep that in mind and am tackling a programming problem I'd like to solve optimally. I have a register $32$ bits wide at any one time only $16$ bits(flags) can be set I would like to calculate the number…
DeveloperChris
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Odds of winning division 1 Powerball

The odds of winning division 1 Powerball is stated to be $134490400:1$. That is, you guess the exact draw of 7 unique balls from a drum with 35 balls, and the correct Powerball from another drum that has 20 unique balls. Source I can't figure out…
Freddy Mcloughlan
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How to calculate unique combinations that with fixed positions

I am not that great at math, but am still interested in how one would go about calculating the following question: Employees can type in their access code. There are two sets: A,B,C,D,E and 1,2,3,4,5. An access code looks like this: E314. So always…
stijuh
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Regarding permutations of distinct objects in 3x3 grid

Suppose I have a 3x3 grid and the integers 1 to 9 inclusive. I want to find out how many ways are there to arrange the numbers. My question is: Do I need to account for double counting? | 1 | 2 | 3 | | 4 | 5 | 6 | | 7 | 8 | 9 | | 3 | 6 | 9 | | 2 |…
Lau Di Qing
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Question concerning calculating Permutations

One of the first things that is taught about Permutations is the fairly simple method for calculating how many possible permutations there are. Simply take the number of "events" (eg. the number of characters in a password, the number of bingo balls…
Dicerson
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In a Multiple Select Question, there are 4 options of which one or more can be correct. What is the cardinality of E?

In a Multiple Select Question, there are 4 options of which one or more can be correct. Let us define an event E that the option ‘A’ is correct. What is the cardinality of E? MSQ Options are $= {A, B, C, D} $n(E1)= \{ A \}$ is $1$ Only $A$ is the…
Abbas
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permutation question that has an "at least" restriction?

How many ways are there to seat six boys and seven girls in a row of chairs so that none of the girls sit together? 13P13 - (7P2x11P11 + 7P3x10P10 + 7P4x9P9 + 7P5x8P8 +7P6x7P7 + 7P7x6P6)
T S
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Kendall tau distance and inversion count

The Kendall tau distance between two permutation is the number of index pairs, for which the two permuations disagree in their order: $$K(\alpha, \beta) := |\{(i, j): i < j.\quad [\alpha(i) < \alpha(j) \wedge \beta(i) > \beta(j)] \vee [\alpha(i) >…
tierriminator
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Prove that it is impossible to obtain a new string "B" from an original string "A".

A "string" consists only of the characters "A", "B", "C", and "D". An example would be ABBDCA. Another example could simply be "D". The below rules are the only ways for us to change the string: A substring of AB or BA can be replaced with C and…
MathIsCool
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Proof of Permutations

With repetition allowed, You multiply the r number of times for total n objects n * n * n ... When the repetion is not allowed then you take away an object each time n * (n - 1) * (n - 2) .... So where does the proof come from that you have to…
user753214
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