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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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Number of Ways to arrange things

Please help me with this question because i just don't understand it. A panel is conducting an interview on six candidates of different heights. If they are to put them in line, in how many ways can they arrange them in line such that no three…
Mapoz
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how many odd numbers can be form using 8, 5, 2

calculate how many different numbers can be formed by taking one, two or three digits from the digits 8, 5, 2. How many of these will be odd numbers and greater than than 250? no repetition allowed. i have worked out the first part and i found 15,…
Gibbons Muselitata
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How many 8 digit numbers are there, such that they are divisible by 9 and all of the digits are distinct?

What I'm looking for here is not the answer, but a way to approach this question to get to the answer. Actually, there are some answers where this question was posted, but they are hard to understand. I do see that apparently the answer lies in the…
Garth Marenghi
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Perfoming permutation count

I have a question, probably relatively simple one. Once you want to find all the unique combinations of number 5 you count 5! = 120. Once you want to find all the combinations including repetition of value of number 5 you count 5 power of 5 =…
ucas
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How many permutations of 11 elements are there, from a set of 12 elements with $3$ a's, $3$ b's, $3$ c's, and $3$ d's?

Let $S=\{a,a,a,b,b,b,c,c,c,d,d,d\}$. Determine the number of $11$-permutations of the set $S$. What's the number of ways to take 11 objects from this set S with 12 objects, such that the order of the objects does matter? I'm not sure if…
TAPLON
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A NASCAR race has 53 drivers racing on Sunday. How many different combinations are there for 1st, 2nd, and 3rd place?

A NASCAR race has $53$ drivers racing on Sunday. How many different combinations are there for 1st, 2nd, and 3rd place? Using combination in statistics, shouldn't the answer be $23,426$? Is this correct? ${_{53}\mathsf C}_3 = 23,426$.
buzzard
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couple wedding seating problem

At a wedding party, 'N' couples are invited. A seating arrangement plan has to be formed for them. The problem is, couples either want to seat husband and wife together, or couples can sit between the husband and wife of another couple. Also, people…
ram
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selection of a committee for a group of 8 men and 8 women

From a group of 8 men and 8 women, 4 persons are to be selected to form a committee so that at least 1 man is there on the committee. In how many ways can it be done? ( this is a repeat question ). I found 2 solution to this: 1. combination of (1…
SUBHASH BISHNOI
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How many different 3-digit numbers can be formed if the number can consist of the digits from 0 to 7, cannot start with 0 and must be even?

Original question: A 3-digit number is made up using the digits 0, 1, 2, 3, 4, 5, 6 and 7 at most once each. The number cannot start with 0. How many different numbers can be formed if the number must be even? Approach: Working backwards, there are…
Mad Banners
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Confusion about permutations of "HOME" with vowels together

I have a confusion regarding a question: we are given the word "HOME" and we have to arrange its letters so that the letter "H" always comes first. My concept is to take four chairs on which these four persons are to be seated so that person "H"…
Neeraj Sharma
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Permutations (Making numbers from digits)

Using the digits 1, 2, 4, 5, 7, and 8, how many different three-digit numbers can you form if each digit may be repeated any number of times in a number? I have tried to do this question and tried to find the answer, unfortunately all the answers…
Iolana Eaggle
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In how many ways can students sit

There are N students numbered from 1 to N standing in front of N chairs numbered from 1 to N. What is the number of ways the students can sit such that they don't sit on their own chairs? Student i cannot sit on chair i in none of the…
User_Targaryen
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$p=\sigma \tau^{-1}$ fixes each element of the set $\{a_i : i ≤ j\}$?

I'm trying to understand the proof for Let $\sigma$ be any element of $S_n$. Then $\sigma$ may be expressed as a product of disjoint cycles. In this proof (p. 3) there's a part where $p=\sigma \tau^{-1}$ is said to "fix" each element of the set…
mavavilj
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How can I simplify this number theory problem?

Let X = {1, 2, 3, 4, 5, 6} and σ= \begin{bmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 6 & 4 & 3 & 5 & 2 & 1 \\ \end{bmatrix} Define a relation ∼ on X as follows: for x, y ∈ X, x ∼ y if there is a natural number k such that $σ^k(x) = y$. Prove this…
TheMathNoob
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Number of recursive permutations of all sizes

Consider you have a set of $n$ elements. Now, create all the possible permutations of $k$ elements. Finally, for each permutation create all the possible combinations with the permutations of the remaining $n-k$ elements of the original set…
Arcanefoam
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