Mathematics Stack Exchange
Mathematics Stack Exchange

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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There are 6 people including Carl and John. In how many ways can they arrange such that at least three people will be behind John and Carl?

There are 6 people including Carl and John. In how many ways can they arrange such that at least three people will be behind John and Carl? I have no clue about what to do right now. Could you assist me? Regards
Mark
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The number of ways of selecting $n$ cards out of unlimited number of cards bearing the number $0,9,3$

If the number of ways of selecting $n$ cards out of unlimited number of cards bearing the number $0,9,3$ so that they can't be used to write the number $903$ is $93$ then $n$ is
juantheron
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A five-digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?

I have solved the above question but I found another method for it on a website but didn't understand. Alternative method: The sum of all the numbers formed by the digits a1, a2, a3,……….an, without repetition of the digits is given by: (n-1)!(a1 +…
user25614
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Struggling with writing the diagram mathematically

There are $5$ chemistry and $4$ physics books. How many ways can these books be arranged in a manner that physics and chemistry books will be among themselves? By visualizing what question wants me to do, I drew a diagram as illustrated below.…
Mark
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Circular Permutations

According to page http://tutors4you.com/circularpermutations.htm If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by (n-1)!/2! But how it can be correct? For example when n=1…
user1779660
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The no. of $4$ Digit no. that contain the Digit $6$ exactly once , si

The no. of $4$ Digit no. that contain the Digit $6$ exactly once , si My Try:: We Will take the no. from $\left\{0,1,2,3,4,5,6,7,8,9\right\}$ Now for $4$ Digit no. Case (I) If no. is of the form $\boxed{6}\boxed{+}\boxed{+}\boxed{+}$. Then We can…
juantheron
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Permutation( ordering backpackers in hostels)

Question : five backpackers arrive in a city where there are 5 youth hostels How many different accomodation arrangements are there if there are no restrictions on where a backpacker stays ? I tried this but I can't seem to get your answer in the…
user122343
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Permutation with no two vowels next to each other

Question : find number of arrangements of the word TRIANGLE in which no two vowels are next to each other. My attempt : $5! ( ^6P_3) =14,400$ Is this correct?
user122343
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Permutations Problem (Counting Topic)

For the question below, I have worked out the solution for a) in which I've got: $9\cdot8\cdot7\cdot6\cdot5 = 15120$. However, I am struggling to solve part b) of the question. Any help would be appreciated! The question: Nine boxes are each…
FriendlyMan18
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Using the digits 1 to 6, how many 3 digit numbers can be formed that are divisible by 3?

I can't seem to wrap my head around this problem.How do I make sure that the digit 0 and digits from 7 to 9 are not included ? Provided- Repetition of digits is allowed.
Master Maxx
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Permutation ( selection of 4 letters from 12)

Question : how many different selections of four letters from the twelve letters of the word REFRIGERATOR contain no R's and two E's? My attempt: If there are to be no R's then the selection is limited to E F I G E A T O (2 . 1. 6 . 5) = 60…
user122343
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Counting permutations with additional requirements

Say I have a set of 36 objects 0-9A-Z. I want to find out how many different orderings of a dozen selections I can make. This is just 36P12, which is a large number. However, I have two scenarios with their own additional conditions: The 12…
MrPuzzler
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Permutations Seating Arrangement in Group

As per the question, I think the answer is $2\times4! = 48$ ways, but unable to visualize how they are seated in?
Dinesh Potluru
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How to work out the number of ways a user can be asked to enter 3 characters from a memorable word.

A bank when you sign in asks for a Userid and a Password and when accepted asks for 3 characters from a previously registered memorable word. The numbers of the characters are always in ascending order. Example 1,4,7 or 5,6,7 but never 1,7,4 or…
MacNala
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Linear Permutation of Grouped Things

I can not search this over the internet so I thought some of you guys can help me out. The question goes like this. There are 15 books. Of these are 5 Mathematics, 7 Physics, and 3 books on Chemistry. In how many ways can they be arranged in a…
Ardie Burigsay
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