# Tagged Questions

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### Envelopes and Mailboxes

We suppose $n$ and $p$ are two positive integers. A) In how many ways can you divide $p$ identical envelopes in $n$ mailboxes? (Each mailbox can hold several envelopes at the same time) B) In how ...
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### Probability of item distribution with a restriction

I'm having a hard time analyzing my research data, and was wondering if anyone had any suggestions? I've reworded the question so it is presented more like a statistics problem. There are $x$ number ...
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### What is this probability that this event could occur?

Records show that 30% of the people, listed as passing the Firefighter's exam in Denver, are republican; the remainder as democrats. Last year, 30 people were hired as firefighters for the city. (25 ...
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### Calculating probabilities for distributing M balls in 4 bins scenario

I have the following scenario that I need to obtain the formula for it in order to program it: There are number of balls (M balls), and there are 4 different bins (Bin1, Bin2, Bin3, Bin4) that the ...
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### Permutation and combination regarding two people together

You have 11 friends and can invite 5 to dinner 1) in how many ways if two of the friends married and will not attend separately? 2) in how many ways if two of them are not on speaking terms and will ...
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### Permuation & combination on finding number of ways lid can be wrongly placed

There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the ...
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### What number of robbers, under the model of the prisoner's dilemma, would be optimal?

The prisoner's dilemma is defined as "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with ...
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### Probability [Sum of digits is even for a random number] [closed]

A number of 6 digit numbers is written down at random. Probability that the sum of the digits is an even number is? Please answer with explanation.
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### Probability [Distinct balls in distinct boxes]

6 different balls are put in 3 different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is ? Could anyone pleases give the answer and explain it.
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### How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4 (if repetitions are not allowed)?

My Approach: Total no of available digits: 5 No of 1-digit formed: 5 No of 2-digit formed: 4(excluding '0' on ten's place) * 4 (including zero - one among given digits already used) No of 3-digit ...
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### Mary can answer 20/25 problems correct… simple probability

Question: A teacher gave his class $25$ problems and told his students that he would select $10$ of them to put on their midterm. Mary can figure out how to answer $20$ of the problems, what is the ...
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### Multiple Hypergeometric Distributions

I need to figure out a problem which involves multiple hypergeometric distributions. Referring to the Urn problem, the problem can be described like the following: We have $n$ urns $u_1,…,u_n$. Urn ...
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### Largest Number Drawn - Why are These Approaches Not Equivalent?

Here's the question: Four numbers are drawn at random from a box of ten numbers 0, 1, ..., 9. Find the probability that the largest number drawn is a six if the draws are made with replacement. The ...
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### determining the amount of total questions needed in a game given the probabilty

I'm creating a game and can't seem to quite figure this out - driving me crazy. There are 8 questions in my game You can play the game an unlimited amount of times the test bank doesn't change. so ...
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### Probability of two digit number sequence in series of numbers

Given a random sequence(say $15$) of numbers I want to find the odds of finding '$90$' and '$09$' in the sequence. Looking at just two numbers in the sequence you have a $\dfrac{2}{10}$ chance of ...
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### Give a combinatorial argument to show that C(n,k) = C(n,n-k)

What is combinatorial argument and how can i prove this equation ? As far i understand i think we have to apply the Chu-Vandermonde identity but i am not sure if thats right or not. ...
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### In how many ways can 20 identical balls be distributed into 4 distinct boxes subject?

I was practicing math exercises on text book and i got stuck in this question ? ...
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### Outcome possibilities with three teams and three outcomes for each game

So there are six teams (let's say: 1,2,3,4,5,6), and they pair up to face each other, (so three games in total). In each game, one team either wins or their is a tie. Let's set up the teams and their ...
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Suppose that a password for a computer system must have at least 8, but not more than 12, characters, where each character in the password is a lowercase English letter, an uppercase English letter, a ...
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### Expected Value of this function

Let’s consider a random permutation p1, p2, …, pN of numbers 1, 2, …, N and Function F is calculated as F=(X[2]+…+X[N-1])^K, where ...
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### Number of permutations for n elements with different probabilities

I'm studying the paper Database-friendly random projections: Johnson-Lindenstrauss with binary coins by D. Achlioptas and can't manage to work out the total number of permutations with repetitions in ...
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### Expected Value of Local Maxima and Local Minima

Recently I came across this question: Given a random permutation of integers 1, 2, 3, …, n with a discrete, uniform distribution, find the expected number of local maxima. (A number is a local maxima ...
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### What is the number of permutations for given N numbers, such that the first part is non-decreasing?

Let $A$ be a list of $n$ numbers in range $[1,100]$ (numbers can repeat). I'm looking for the number of permutations of $A$ which start with a non-decreasing part, where this part ends with the first ...
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### Exotic 6-horse race betting probabilities

I'm gearing up for horse racing season, and I'm trying to teach some fellow engineering friends how to bet "exotic" bets by using colored dice to simulate horses. So, the odds for each horse winning ...
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### Probability and combination/permutation help? [closed]

So, I need some help on a few problems. This isn't my homework. I'm preparing for a test and these are just some of the practice problems. I have the answer for them but I don't understand how to get ...
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### Probability of all objects not in order

There are four envelopes and corresponding $4$ letters.If the letters are placed in the envelopes at random,what is the probability that all the letters are not placed in the right envelopes? ...
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### Proof for the probability that $A[i]<A[j]$ in a random permutation

I'm studying a proof on the expected number of inversions in a permutation of $n$ numbers. The numbers are distinct integers from $1$ to $n$. At some points it takes as given that chosen two indices ...
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### What is the probability no slots contain more than two balls given I am trying to sort 5 balls into 6 slots?

I am having a difficult time understanding how to approach this problem. Suppose I have $6$ total slots and $5$ balls. Now, I assign the balls at random to the slots. What is the probability that no ...
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### What is the probability of winning.

$2$ teams of $5$ players each play a game against each other in pairs. Find the probability that no team wins all the games and no team loses all the games. I tried to solve and determined that there ...
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### Probability/selection problem

Assume that we have $N$ items of $M$ distinct types in a closed bag. We also have $K$ bowls $(K \leq M)$ that can hold only items of same type. In the beginning bowls are empty. And bowls can hold a ...
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### Four Children Combination Problem

This is a problem that has haunted me for some time There is two family. First Family : ...
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### Probability of X winning N number of games

Say there is a player X. X has to choose and play one of the 4 games - Game A, Game B, Game C, Game D ...
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### permutation problems

Two professors are scheduling separate individual exams for 12 students in the same hour. Examination of one student in each subject takes 5 minutes. In how many ways can this scheduling be made? ...
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### In a standard deck of 52 cards, how many different 7 card hands are there in which 3 cards are hearts and the other 4 are of different suits?

I know there are 13 cards in each suit, so that would mean I needed 3 of the 13 hearts or 13 P 3, then the other 4 would need to be out of 39 so it would be 39 P 4 but I don't know where to go from ...
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### Permutations and Combinations.

There are 4 red and 6 blue marbles in a bag, 3 are picked out at random, what is the probability that atleast one of them is red? My answer is 1/2 First I calculated the total number of ways that I ...
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### Finding probability of earning points

A professor asks a true/false question with ten individual questions. Suppose the professor assigns grades of: $10$ points for each correct response, $0$ points for each absent response, and $-10$ for ...
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### Help with Discrete Probability

I'm trying to show statistics related to combinations of discrete variables. I have a feeling what I need to do is quite simple but I can't for the life of me remember the correct formulas to achieve ...
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### Number of permutation

I can't guess how to compute number of permutations when I have $f$ fields and number $a$ of elements to distribute among them. Such that sum must be equal to $a$. Could you enlighten me and refer to ...
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### Probability of the sum of two drawn cards being less than 11?

An Ace has a value of 11 in this problem, and a face card has a value of 10. Thus, my idea for solving this problem was to separate the problem into 7 different cases (drawing a 2 first, 3 first, 4 ...
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### Permutation query involving 3 people with a limit of 45 as the sum.

I'm looking to find all the combinations of numbers possible in the below example. I shall do my very best to explain the situation clearly as I'm not too sure how to derive this outcome myself. ...
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### permutations rolling die 6 times [closed]

How would you calculate the probability that if you roll a six sided die six times you will roll 1,2,3,4,5,6 consecutively. I am totally lost on how to even calculate this.
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### Calculating the expected profit with Probability A level maths CIE

Company sets up display of 20 fireworks! for each firework, the probability that it fails is 0.05,independently of other fireworks the probability that more than 1 firework fails is 0.264 the 20 ...
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### What is this the name of this idea? (combinatorics)

The problem: There are three screws, each one a different type {Phillips, Robinson, Slotted}. There are three sets of screwdrivers, each set corresponds to a type of screw. There are no two ...
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### How many ways to arrange $20$ items on $4$ towers

Suppose you have $20$ different rings and $4$ display towers. On each tower the rings are stacked one above another. In how many ways can they be arranged if: [a]: The order of rings on each tower ...
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### In how many ways can four students be chosen from a group of 12 students?

Myself and my Math teacher are at a disagreement in to what the proper method of solving the question In how many ways can four students be chosen from a group of 12 students? is. The question comes ...
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### How many triangles can be made with those holes?

A 5 by 5 square lattice is formed by drilling holes in a piece of wood. Three pegs are placed in this lattice at random. Find the probability that three randomly chosen points of a 5 by 5 lattice ...
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### Possible combinations of digits

What is the probability that a random $r$-digit number $(r \geq 3)$ contains at least one $0$, at least one $1$, and at least one $2$? My initial guess was $1-(\frac{7}{10})^r$ seeing that it's $1$ ...
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### Number of ways of arranging numbers with given max difference

How many ways are the there to arrange n numbers out of m numbers (1 to m) so that the difference between the max and min numbers of those n numbers is D which is given. For example : n = 4 m = 3 ...
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### Getting K heads out of N biased coins problem (formula generation ).

Problem- Given a set of coins n with each coin i having Pi probability to give heads. Find the probability of getting k heads, when all coins are tossed together. hi i have solved this problem ...
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### A fair die is rolled eight times. What is the probability of getting exactly 2 threes, exactly 3 ones, and exactly 2 sixes?

I was given the following hint: Break the task of counting the desirable outcomes into three subtasks: (a) choose the location of the extra non-three, one, or six in the sequence of eight throws, ...