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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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Suppose that all licence plates consist of three symbols chosen from the 26 letters of the alphabet followed by three or four of the digits 0-9.

(a)How many license plates are possible if repetition of symbols is allowed? I separated the two equations to show the two different cases (three or four of the digits case) This is what I got: (26^3)(10^3) + (26^3)(10^4) (b)How many license…
Blue Lightning
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4 digit numbers divisible by 11

Four digit numbers are formed using the digits 1,2,3,4 (repetition is allowed). The number of such four digit numbers divisible by 11 is- (1) 22 (2) 36 (3) 44 (4) 52 I know for a number to be divisible by 11 the sum of digits at even places must be…
CodeBlooded
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Rearranging digits for multiples of 4

How many ways are there to arrange the digits $1,2,3,4,5,6,7$ so that a $7$ digit number is formed, such that the number is a multiple of $4$. I know that when the second last digit is an odd number the last number must be "$2$" or "$6$".…
Tawfek A
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No. of four-digit even numbers formed by digits 0 1 2 3 4 5 without repetition

I started from the units. There can only be $3$ possibilities $0,2,4$. Then there are $5$ possibilities for the tenth place. THen there are $4$ possibilities for the hundredth place. Then only $3$ possibilities remain. Thus the permutation is $3…
MR. Raindrop
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Given $4$ places, find the number of ways you can fill four Reds, one Blue, one Green and​ one Yellow

Given $4$ blanks, find the number of ways you can fill four Reds, one Blue, one Green and​ one Yellow so that none of the blanks is filled up with $4$ reds and none of the blanks remain empty. I cannot get the final answer. All I can do is find the…
Mathejunior
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Trouble understanding permutation problem

This is a solved problem in "Introduction to Probability", 2nd Edition, by Bertsekas and Tsitsiklis, example 1.29, page 47. I'm having trouble understanding the answer to the second part. You have $n_1$ classical music CDs, $n_2$ rock music CDs,…
AnonymousUser
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List all size $4$ subsets from the set $\{A,B,C,D,E,F\}$

List all size $4$ subsets from the set $\{A,B,C,D,E,F\}$ So first I realized this is a permutation because subsets are the same off they have the same elements. So to figure out how many subsets there would be 6p4 which is 15. However I am having…
Lil
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Permutation does not change if we multiply by left by another group element?

Let $(G=(a_1,...,a_n),*)$ be a finite Group. Define for a element $a_i \in G$ a permutation $\phi = \phi(a_i)$ by left multiplication: $$ \begin{bmatrix} a_1 & a_2 & ... & a_n \\ a_i*a_1 & a_i*a_2 & ... & a_i*a_n \\ \end{bmatrix} $$ I am struggling…
laguna
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Permutation on batting

Question - A baseball manager insists on having his best hitter bat fourth and pitcher bat last. In such circumstances how many batting orders are possible? A baseball game must have 9 players with 9 specific spots and having 2 players already…
Dave
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3-letter arrangement for "silly" - Permutations homework

We a homework question that asks us to find the 3 letter arrangement of the word "Silly". Here is the exact question. How many three-letter arrangements are there of the letters taken from the word SILLY? What I did was do $5P3/2!$ and I ended…
Jeel Shah
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Circular permutation on seating

There are 21 people ,15 boys and 6 girls.how many ways are there to seat at least 2 boys between any two adjacent girls in a round table?. I get my answer 708480.i m wrong ,i think.please help me.
Khant Si Thu
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Number of deranged indices

For a permutation $\sigma = (\sigma_1,...,\sigma_n)$ of the numbers $\{1,...,n\}$ a deranged index is an $i$ such that $\sigma_i \neq i$. We know how to count deranged permutations (permutations that $\forall 1\leq i \leq n : \sigma_i \neq i$) and…
TheNotMe
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A doubt regarding circular permutations

In my textbook it was given that the number of circular permutations of n different things taken r at a time (regarding anticlockwise and clockwise arrangements as different) is (nPr)/r. Any help regarding its proof will be appreciated.
Abcd
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Counting possibilities

There are 4 different sports which are to be played on a seven day program such that on each day exactly one sport can be played. If Mr D must play at least two sports on at at least three days each, in how many ways can he schedule the program? My…
Ajax
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Next greater permutation where a given index is changed

Suppose we have the set $\{1,...,n\}$ and we are given a permutation of its' elements, say for $n=4$ we have $3214$. Then we are given an index $i$ (say indexes go from $1$ to $n$) and we are asked to find the next smallest permutation that is…
TheNotMe
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