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.

12854 questions
-1
votes
2 answers

Quintary Sequences

Can anyone tell the answer for this question and explain it in simplified form? Find the number of n-digit quintary sequence (sequence made up of the digits 0, 1, 2, 3, 4) that contains an even number of 1s?
-1
votes
2 answers

How many integers can be formed by using exactly $x$ $4$'s, $y$ $5$'s, and $z$ $6$'s if no other numbers are used?

Can anyone tell me the total number of integers than can be formed by using exactly $x$ $4$'s , $y$ $5$'s and $z$ $6$'s and no other numbers are used? For $x=1$, $y=1$, $z=1$, the total is $6 \implies 456~465~654~645~546~564$? In general, what can…
-1
votes
1 answer

difference of at least 4 between two numbers

In how many ways we can select two numbers from first $10$ natural numbers so that difference between them is at least four? If we select the numbers from the interval $[1,10]$, will the answer change? Here $[1,10]$ means the interval containing…
-1
votes
2 answers

can anybody help in finding number of ways the letters of the word 'PERMUTATION' be arranged so that consonants are in alphabetical order?

I had tried the question and got the answer 11!/(6!2!) but the answer given is 11!/6! if any body can explain that why 2! is not in the answer or the answer is wrong.
Nikita
  • 3
-1
votes
1 answer

Number of pairs of strings satisfying the given condition

We are provided with a string A (may contain repeated characters as well ). One needs to make all possible permutations of A , and find out how many pairs of strings chosen from these permutations are not similar. Two strings are similar if we can…
-1
votes
3 answers

Number of 5-digit numbers

Question: Construct 5-digit numbers from the digits $0, 1, 2, 3, 4$. Repetition and $0$ at the beginning isn't allowed. a) How many 5-digit numbers can be formed? b) How many of these are odd? c) How many of these are divisible by 5? For a), I got…
Giorgos
  • 29
-1
votes
3 answers

15 indistinguishable fishes be placed into 5 different ponds

In how many ways can 15 indistinguishable fishes be placed into 5 different ponds, so that each pond contains atleast one fish? I am struck on this problem.Can someone help me out please.
manu
  • 43
  • 4
-1
votes
1 answer

Permutations regarding $3$ women and $4$ men

$3$ women and $4$ men are standing in a line. If no two women may be adjacent to each other, how many distinct line-ups are there? I'm not sure how to do this. I know $4! = 24$ and $3! = 6$. Where can I take it from there?
-1
votes
1 answer

Permutations of Characters

How many strings of five characters use the letters a, b, c, d and do not have the letters bad appearing consecutively and in this order? (Letters can occur any number of times, including not at all.)
EmaLee
  • 1,153
-1
votes
2 answers

How many ways to divide 11 people into 3 groups of 3 and one group of 2?

How many ways are there to divide 11 people into 3 groups of 3 and one group of 2? The right answer is 15400 but I can't get it
-1
votes
2 answers

Count how many numbers containing number 4 among the numbers 1 to 8900?

I Got a Problem like this "Count how many numbers containing number 4 among the numbers 1 to 8900 ?" what is the appropriate formula to solve the problem above, I tried to solve it by creating a looping algorithm as below function…
-2
votes
2 answers

Combinations of the word REMEMBRANCE

4 letters must be chosen from the word REMEMBRANCE How many different selections can be done if there is no M, no R and at least 2 Es? I've seen this question somewhere but i don't remember the question well i know that the answer is either: (3c2 x…
-2
votes
1 answer

Distinct Permutation

How many distinct arrangements can be made from: -advisor -woodworker I think advisor would be 7! and woodworker would be 10! or does woodworker count differently because of the repeated letters?
-2
votes
2 answers

Numbers are formed using the digits $1,1,2,2,2,2,3,4,4$ taken all at a ...

Numbers are formed using digits $1,1,2,2,2,2,3,4,4$ taken all at a time. Find number of such numbers so that odd digits occupy even places. The odd digits are $1,1,3$ and there are 4 even places So permutation of arranging 3 items in 4 places…
Aditya
  • 6,191
-2
votes
1 answer

Calculating number of non-duplicated permutation

I want to calculate the number of permutation from duplicated list. Example) There is a list combined of 76 icons. Here is icon list A: 1 B: 3 C: 5 D: 6 E: 6 F: 5 G: 10 H: 9 I: 8 J: 7 K: 6 L: 10 In this List, I want to pick 3 icon and make a…