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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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Calculating number of winners possible for an archery competition.

There are ten contestants in an archery competition. Four of the contestants are women. Prizes are awarded to the top four competitors. If at least one woman finishes in the first four places, in how many ways can the top four places be filled?
Josh
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Permutations: Upgrades and Downgrades

I'm working on a game. In the game, all the pieces have stats, like "Strength", "Smarts", "Skill" etc. Any of these stats might be above or below the baseline. I want to work out how many permutations of stats I can have if I've settled on the…
baudot
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How many 3-digit numbers can be formed using the digits 2, 3, 4 and 5 as often as desired?

The method I tried: 5 x 4 x 3 = 60 different numbers I solved it this way because if a number needs to be formed with a certain number of digits (with no restrictions - which I think 'as often as desired' means), you assign a scale to the given…
Mad Banners
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In how many ways a number $\gt 5000$ can be formed using given digits without repeating?

In how many ways one can form a number greater than $5000$ when allowed only to arrange digits taken from $2,3,4,5,8$ without repeating any digit? I would think it would be $2\cdot4\cdot3\cdot2$. Would this be correct?
fosho
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Permutations & series

Consider all the $7$ -digit numbers containing each of the digits $1,2,3,4,5,6,7$ exactly once, and not divisible by $5$. Arrange them in decreasing order. What is the $2015$th number (from the beginning) in this list?
mnulb
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permutation basic concept confusion

I have searched on many sites on internet but no one answered my question.. although question is not so different but as i believe in learning concept rather than memorizing it. I want to know why we multiply in case of permutation. Like if i want…
Neeraj Sharma
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The product of $(a_1-1)(a_2-2)....(a_{169}- 169)$ is

Let $a_1,a_2,.....a_{169} $ represent any arbitrary permutation of the number $1,2,3....169$. Then the product $(a_1-1)(a_2-2)......(a_{169} - 169)$ is Odd only for some permutation, not all Always even, whatever be the permutation Always odd,…
Aakash Kumar
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Permutation formula for lock combination

I know the basic permutation formula for k objects out of an n set. But what is the formula for determining the number of permutations where k is a range (1..m) ? What are the formula for the following scenarios? 1) a keyless door lock has n…
MarkE
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Number of ways to have $N$ as sum of $K$ numbers such that one of them is odd

I want to know if there is a formula to find the number of ways to express $N$ as sum of $K$ non-negative numbers such that at least one of those $K$ numbers is odd. Example: if $N=2$ and $K=3$ the answer is $3$: $(1,1,0)$, $(1,0,1)$,…
Sayan Ghosh
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how many ways is it possible to seat eight people at a round table ...

I know this is a permutation problem, selecting two from eight. My problem is how to use this information: "must sit one seat away from each other." In how many ways is it possible to seat eight people at a round table if Alex and Bob must sit one…
learning
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Demonstrate that the product of the permutations(regardless of order) of $S_4$ is not equal to $a$

$S_4$ is the set of all permutations of length 4 Let $a=\binom{1\,2\,3\,4}{3\,2\,1\,4}$ I found that $a$ is an odd permutation and I want to demonstrate that the product of the permutations is even but Im not sure if this is true and I have no idea…
oren revenge
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3 men have 4 coats , 5 waistcoats and 6 caps. Then in how many ways can they wear them?

The question is in the title itself. First, I would like to share how I solved this problem at first: We have $4$ coats, $5$ waistcoats and $6$ caps. So, I considered that each man wears one coat, one cap and one waistcoat at a time. So, one…
codetalker
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Dealing with "at least" in Permutation

For the following question (which I pulled of the internet) A five member committee is to be selected from among four Math teachers and five English teachers. In how many different ways can the committee be formed under the following…
MistyD
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Doubt in Circular Permutation: 4 Americans and 4 English are seated on a round table.No Two americans sit together.Find the number of ways.

The question is 4 Americans and 4 English are seated on a round table.No Two Americans sit together.Find the number of ways. So,after this I did: $(4-1)!$ for seating the Americans around the table.And the book says afterwards that the Englishmen…
Ishan Taneja
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sum of numbers formed by permutations

I have digits 2,3,4,5. I have been asked to find the sum of all 4 digits the numbers that can be formed using these digits without repetition such that all are included in the number. Can someone help me solve this quickly? The answer is 93324.
user6037890
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