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 many 4 digit numbers can be formed?

Given digits: 0, 1, 2, 4, 5, 7, 8 and 9 1.How many 4-digit numbers can be formed greater than 3000 without repetition? [Here we mean no repetitive digits] My answer is 5*7*6*5 .How many 4-digit even numbers can be formed greater than 3000 without…
PRD
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How do you solve a permutation question involving repetition AND multiple identical objects?

Question: License plates in British Columbia have the form ABC 123 or 123 ABC. All 26 letters (A to Z) and 10 digits (0 to 9) may be used more than once. How many plates are possible?
John Yu
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Arrangement related question

Question- $5$ boys and $5$ girls to be arranged in a row such that boys and girls are alternate and a particular boy and a particular girl are never together. Try- taking the total number of cases to be $5!×5!×2$ then making groups such as $b2g2$ …
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Permutation group. Show that the group has just three members of length 2 in cycle notation.

Show that there are just three members of $S_4$ which have two cycles of length 2 when written in cycle notation. I'm having trouble figuring out how I should test this. It seems dumb to write out all 24 permutation combinations and then convert…
Elias
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Calculating # of letter permutations that can be rearranged without having letters that are repeated adjacent within the sequence of letters

I am not a math expert, but I have been reading about permutations and I am trying to write an algorithm to solve a freecodecamp challenge. My algorithm has passed all the tests except for one test Given a string of letters of 'aaabb', how many…
Eggs
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Reasoning behind count of permutations of the word ROOT

If we need to find permutation of words in ROOT it is $4!/2!$ as $2$ objects are the same. Why do we divide by $2!$ and not subtract $2!$?
user58660
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Arranging persons so that any of the ladies and childern does not sit together

In what ways 2 Men and 3 ladies and 2 childern can be sit so that any of ladies and any of childern do not sit together?(however any childern and any lady can sit together) I have solved above question with a different method but I am confused how…
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Find the number of ways to arrange balls

There are $n + 1$ white and $n + 1$ black balls each set numbered $1$ to $n + 1$. The number of ways in which the balls can be arranged in a row so that adjacent balls are of different colors is A. $(2n + 2)!$ B. $2(2n + 2)!$ C. $2(n + 1)!$ D. $2((n…
Nimmi M
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Used 5 colors for making a 12 X 6 matrix. Is their a software to depict the combinations?

I have used $5$ colors for making a $12 \times 6 $ matrix. What are the possible combinations? Is there a software to depict those combinations? Thanks
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How many possible 3 character combinations using letters?

How many combinations can be using 3 alphabet letters (from A to Z)? Note that string doesn't have to be unique, it can be eg. RPP or AZZ
zarkoz
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Number of ways the letters of "Arrange" can be arranged so that the two r's are not consecutive

Show that the number of ways in which the letters of the word "arrange" can be arranged so that the two r's are not consecutive is $900$.
sophin
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Permutation...Help Needed

The letters of the word CAMBRIDGE are arranged such that the first five letters of the alphabet are in alphabetical order. Find the number of different permutations. [ANS: 3024] Only permutation should be used. Two Families, each consisting of the…
Zolo
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Permutations and Combinations Question.

No. of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly 4 girls stand consecutively in the queue? The image of the question can be seen on the link below. It is google link as I can't upload image. Q44 of the pic is…
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Five balls are to be placed in 3boxes

Five balls are to be placed in 3boxes such that balls are different but boxes are identical
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number of ways to make a selection

In a book I saw a paragraph , but I cannot understand what is the logic behind that Can anybody explain me this .