For questions related to permutations, which can be viewed as re-ordering a collection of objects.

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1answer
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CAT permutation and combination 5

How many 8 digit numbers can be formed using the digits 1,2 and 3 so that the number contains at least one of each of these three digits?
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1answer
28 views

Counting squares in a given k by k square..

So the question is : The solution to this problem according to the book is to first count the number of squares whose sides are parallel to the sides of this 10 by 10 square and then to count the ...
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1answer
19 views

permutations with a given condition!

What will be the number of permutations of n different things, taken r at a time,when p particular things is to be always included in each arrangement? I know the answer to this question but could not ...
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1answer
24 views

The number of ways of going up 7 steps …

The number of ways of going up 7 steps if we take one or two steps at a time is ? So its essentially asking in how many ways can we make use of numbers of (1,2) to get a sum of 7. Am I wrong up till ...
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3answers
59 views

In how many ways can you choose three distinct numbers … [on hold]

In how many ways can you choose three distinct numbers from the set of {1,2,3,...,19,20} such that their product is divisible by 4 ?
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3answers
46 views

How many digits… [on hold]

How many $3$ digit numbers of distinct digits can be formed by using the digits $1,2,3,4,5,9$ such that the sum of the digits is at least $12$ ?
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1answer
19 views

Number of arrangement

Problem: What is the formula of number of arrangements? More specifically I need to avoid repeated elements and the order of the sequence does not matter. For lucidity I show an example: For 3 ...
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1answer
9 views

permutation game labels

A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only. How many ...
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0answers
29 views

Color Cyclic Permutations

Suppose there are n people sitting in a circle,wearing 3 kind of shirts viz. white,red and green. When two people with different shirt color talk with each other, they both change their shirt to ...
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2answers
78 views

A simple question in combinatorics.

A university bus stops at some terminal where one professor,one student and one clerk has to ride on bus.There are six empty seats.How many possible combinations of seating? My problem:I know that if ...
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0answers
31 views

Arrangement of 4 boys and 4 girls with no two girls are next to each other?

Let we have 4 boys and 4 girls and we need to arrange them, with no two boys and no two girls are next to each other? Let place first the boys b b b b the 4 ...
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0answers
18 views

Question regarding permutations and combinations? [duplicate]

Hi, I was just wondering on how you are supposed to approach this question. I keep getting 114 as an answer, but the answers say it is 174. How would anyone do this question, because I feel like I'm ...
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3answers
52 views

Question regarding permutations and combinations?

Hi, I was just wondering on how you are supposed to approach this question. I keep getting 114 as an answer, but the answers say it is 174. How would anyone do this question, because I feel like I'm ...
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1answer
64 views

Counting possible combinations to open a lock( 2006 ACM ICPC)

I was working on a problem in a coding competition and I began to wonder about the analytical (mathematical) solution to this problem. I am not even sure how to go about counting this. Any ideas will ...
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2answers
74 views

please help me ( probabilities )

please let me know if my answer true or false Three numbers are chosen at random without replacement from the set {0, 1, 2, 3, ... , 10}. Calculate the probabilities that for the three numbers drawn ...
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0answers
16 views

A question on restricted permutation 1

In how many ways can $m$ white balls and $p$ black balls be arranged ($m>p$), so that no two white balls are together? Can the solution be generalized? Consider $k$ different colored balls ...
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2answers
15 views

Permutation of objects selected from a group

I'm having trouble with this question: How many numbers greater than 300 can be formed from the figures 4, 3, 2 and 1 if each figure can be used no more than once in each number and all the ...
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1answer
72 views

How to find out the number of ways to solve Instant Insanity

Problem : We are given 4 cubes. The 6 faces of every cube are variously colored - Blue, Green, Red or White. Stack the cubes on top of another in such a way that no color appears twice on any of the ...
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0answers
27 views

Inversion and permutations

Let call two arrays A and B with length n almost equal if for every i (1 <= i <= n) CA(A[i]) = CB(B[i]). CX[x] equal to number of index j (1 <=j <= n) such that X[j] < x. For two ...
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0answers
16 views

How to represent a problem of choosing one permutation over x different subsets of combinations?

I'm writing a computer program and I have problems understanding how to iterate this problem: 3 independent sets of numbers where I need to choose two out of three. That falls under simple category ...
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1answer
20 views

Permutations in circular arrangements

I have another permutation question that I'm having trouble with; this time with circular arrangements: To a meeting involving four companies, each company sends three representatives -- the ...
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1answer
13 views

Permutation/factorial question

I have this question: How many numbers greater than 40 000 can be formed using the digits 2, 3, 4, 5 and 6 if each digit is used only once in each number? The first digit needs to either be ...
0
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1answer
17 views

Relationship between the probability two items in a list are correctly relatively ordered and the probability of any item being in the right place

Given a disordered list a of size n, and an ordering on the items of a, is there a relationship between the probability that two items are correctly ordered ($P(a_i \leq a_j)$ given $0 < i < j ...
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0answers
72 views

Help calculating Combinations

A boy has n objects to paint, ordered in a row and numbered form left to right starting from 1. There are totally c colors, numbered from 0 to c-1. At the beginning all objects are colored in color ...
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1answer
76 views

Place, show and unordered horses forecast probability calculation

given the following horses, each with its chance of winning: Horse 1 -> 0.29 Horse 2 -> 0.34 Horse 3 -> 0.11 Horse 4 -> 0.07 Horse 5 -> 0.14 Horse 6 -> 0.05 Sum -> 1 At the moment, in order to ...
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0answers
56 views

Sum of possible permutations

Lets call two arrays A and B with length n almost equal if for every i (1 <= i <= n) CA(A[i]) = CB(B[i]). CX[x] equal to number of index j (1 <=j <= n) such that X[j] < x. For two ...
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1answer
28 views

How many ways to arrange books? Combination/permutation problem

I'm having trouble solving this question...I'll try to be more specific. The problem could be split into 3 "cases" (4 bio, 3 bio+1 novel, 2 bio+2 novels) I used combination rule for 4 bio case and ...
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2answers
19 views

Counting Problem using Permutations

The Question was: In how many ways can the letters of the English alphabet be arranged so that there are exactly 10 letters between a and z? My approach was the following: In between a and z, there ...
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3answers
28 views

Problematic Permutation Problem

i see a problem without any definition. would you please help me? i want to calculate the number of permutations of 1,2,...,1392 that 696 numbers be in the natural positions (from all numbers, 696 ...
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3answers
72 views

Counting valid tickets

I think my question is very easy but I need to understand. The problem is, I have a ticket with 2 numbers from 1 to 10. The first number cannot be greather than the second number. How many valid ...
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3answers
21 views

Combination & permutation help!

I was thinking: 120 - 5C4 but the answer is 24. Is anyone able to explain this for me?
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0answers
82 views

Arranging numbers in a grid

I have a $n \times m$ matrix $M$ and a permutation of sequence $P$ of numbers from $1$ to $n$. I have to fill the matrix using numbers $1$ to $n \times m$ in such a way that for each row $i$, the ...
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1answer
37 views

How many even numbers greater than 50 000 can be formed from specified digits without repeat?

The digits are 3,4,5,6,7,0 My working is as follows: I realize that you would need to start with either 5,6 or 7. From there you have 5 digits to re-arrange, but the permutation would have to end in ...
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1answer
32 views

Determining the different number of subsets (counting, permutations, combinations)

Given that any fixed integer n>0, let S={1,2,3,4,...,n}. Now a Red-Blue subset of S is called T. Every element of T is given a colour (either red or blue). For instance {17 (red)}, {1 (red), 5(red)} ...
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1answer
43 views

Permutations, Combinations, and Counting

A group of 63 people are camping together. They have two 6-person tents, three 4-person tents, five 3-person tents, and three 2 person tents. 18 people will sleep outside of the tents under a tarp. ...
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1answer
25 views

Permutation and Combinations (Separation) [closed]

Eight students are to be arranged in a row. Find the number of ways to arrange them if three particular students must be separated.
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1answer
53 views

Counting the arrangements of 8 people around a square table?

I am trying to solve this problem of counting the number of arrangements of 8 people around a square table, as shown in the figure below, To solve this problem you can consider arrangements obtained ...
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0answers
21 views

Permutation certification. A cryptographic hash function for permutations?

Alice has a secret permutation $\alpha$ (a random permutation of an $n$-set; $n=18$ would be a decent choice for the application I have in mind). She wants to convince Bob that she has $\alpha$, but ...
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49 views

Devise formula for Finding the number of permutations with repetition whose sum APPROACH a target number

Suppose a given set $s = \{2,3,4\}$ and lower limit $= 7$. I need to devise a formula for calculating the number of all possible permutations with repetition satisfying the following conditions: The ...
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1answer
37 views

Total number of possible sub sequence with given condition

Given a sequence of two letters A and B find the total number of possible sub sequences where number of letter A is two times the number of letter B without ...
3
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1answer
33 views

Another formula for number of onto function.

Let A and B be two sets. $A=\{1,2,\dots m\}$ $B=\{1,2,\dots n\}$ We have to find the number of onto functions from A to B In the following link , the approach of the answer was applying Inclusion ...
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1answer
47 views

number of cycles in a permutation

I have given a permutation let 2 3 1 5 4 that is if initially my string is 1 2 3 4 5 the after one permutation it will become 1 2 3 4 5 3 1 2 5 4 that is the number in first position will go ...
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0answers
45 views

What Will be permutation of this question?

Sereja call two arrays A and B with length n almost equal if for every $\,i (1 \le i \le n), CA(A[i]) = CB(B[i])$. $CX[x]$ equal to number of index $j (1 \le j \le n)$ such that $X[j] < x$. For ...
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1answer
45 views

If matrix $A$ is invertible, then there is a permutation of its rows leaving no-zeros on the diagonal

I need to prove this statement: "If $A$ invertible, then exist a permutation of its rows leaving no-zeros on the diagonal" and I tried using the definitos of invertible matrices and $LU$ ...
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2answers
35 views

Need help in confirming the answer to a combinatorics question?

I need help to confirm my answer for the following question "There is an alphabet of size 40 and this alphabet is used for forming messages in a communication system. If 10 of these alphabets can be ...
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1answer
32 views

Number of ways to order items

How many ways are there to put 10 red and 9 blue balls in a sequence so that for every index the number of red balls up to and including this ball is greater than the number of blue balls? It means ...
3
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1answer
89 views

Is this notation $\prod\limits_{k=k}^n k $ valid for expressing this product? (ways of arranging $k$ things in $n$ places)

I want to express how many ways you can arrange $k$ things in $n$ places. $$\prod\limits_{k=k}^n k = k (k+1) (k+2)\cdots(n-1) n$$ Edit (added) { The example from which I started thinking about this ...
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2answers
33 views

No. of ways to arrange 4R and 3L so that there is exactly 4 times change from L to R or R to L.

I have to arrange 4R and 3L in such a way to know number of times there is 4 changes in the alphabet of sequence. For instance consider the sequence RLRLLRR, this sequence has 4 places where R and L ...
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1answer
33 views

Predict number of Birthdays for 1000 person of same class in next 365 Days

I want to know an approximate number of birthdays for a class where each month 1000 Persons are added up. Like 1st month its 1000, 2nd month its 2000, 3rd month it is 3000 And so on. Now lets say ...
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1answer
50 views

Partition numbers with restriction on the greatest part *and* on the number of positive parts

I’m looking at partition numbers. OEIS A008284 says that the number of partitions of $n$ in which the greatest part is $k$, $1 \le k \le n$, is equal to the number of partitions of $n$ into $k$ ...