0
votes
0answers
16 views

What does a presentation on block design and Latin squares consist of?

I read the wikipedia pages of both and I just cannot understand these two concepts. I have a presentation on both of these topics next week and I need some headway on both of these topics.
3
votes
3answers
77 views

How many ways can $10$ digits be written down so that no even digit is in its original position

If I have the numbers $0,1,2,3,4,5,6,7,8,9$ written down in that order, how many ways can the $10$ digits be written down so that no even digit is in its original position? It would seem that I can ...
1
vote
1answer
104 views

How to convert a problem to a stars and bars problem?

Continued question from here. With certain questions I have $x_i$ being constrained by various different inequalities, I want to know how to remove these from the problem, to bring me back to a ...
0
votes
4answers
35 views

Probability: Linear Seating Arrangement

Okay, I'm new at probability and statistics, so please try to answer this as thoroughly as possible and explain why you did everything, from using a specific number to why using factorials and ...
0
votes
3answers
93 views

How to use stars and bars(combinatorics)

How to use the stars and bars method? Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$ Where $x_i\in\mathbb{N}$ Is this the correct time to apply the method?
0
votes
1answer
32 views

Probability for incomplete information

Let's say there are 10 teams: A-J. Only 1 team wins, others lose. Probability of any team to win is unknown (different for each team) and to be calculated. Not all teams participate in each game. ...
0
votes
1answer
35 views

How to calculate probability that a team will win

Let's say there are 10 teams: A-J. Each team always participate in each of the game. Only 1 team wins, others lose. Probability of any team to win is unknown (different for each team) and to be ...
1
vote
2answers
84 views

Binomial theorem combinatorics derivation

We can split any term $(x+y)^n$ into a choice tree with $2^n$ path choices. Also, we can represent each factor in terms of $x^ky^{n-k}$ It is logical to deduce we can express this with summation ...
0
votes
0answers
163 views

Average deviation of group sizes

I consider $n$ elements randomly dispatched in $n_{G}$ sets. Denoting $s_{j}$ the number of points in set $j$, I then compute the average deviation $d$ as: $$ ...
0
votes
1answer
65 views

Combination Problem with Sofa [closed]

Suppose we have 5 sofa on room A. in this room, 4 students seated on these sofa. These Strudents go to another room for eating dinner, and after that come back to room A. how many way the students can ...
0
votes
0answers
31 views

In how many ways can you make change for a dollar? [duplicate]

I know there are questions related to this on the site but they are not in the context I am looking for (basic statistics). This problem is at the end of the section introducing combinations and ...
1
vote
1answer
74 views

Expected value over many trials

I am a poker player and was talking to my friend about expected value. He claimed that if you play far enough above your bankroll, expected value can be negative, even if you have a skill edge. I ...
1
vote
3answers
33 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 ...
0
votes
0answers
38 views

two correlated process

I apologize if this question is not placed in the right place. But I am having a hard time to figure it out. It would be greatly appreciated if some one could help me out. Assume that there are two ...
3
votes
1answer
64 views

What is the joint probability distribution of number of balls after $n$ draws?

The following problem came into my mind when I am studying the Polya Urn Model. At the beginning, from a bin containing $c_1$ balls labeled $1$, $c_2$ balls labeled $2$, … , $c_m$ balls labeled $m$, ...
4
votes
2answers
93 views

Combinatorics: Mean and Variance of an indicator function of items arranged in a circle.

I have a problem from a homework which I've been struggling with. I normally wouldn't post homework here, but I've spent several hours trying to understand the correct way to solve this , to no avail. ...
5
votes
1answer
71 views

Drawing previously undrawn cards from a deck

Suppose you have a deck of $y$ cards. First, randomly select $y-x$ distinct cards and sign the face of each, then shuffle all the cards back in to the deck. Proceed as follows: Draw a card. If it is ...
0
votes
3answers
32 views

DNA Sequence Distinct Way

we know The genetic code is based on the four nucleotides adenine (A), cytosine (C), guanine (G), and thymine (T). These are connected in long strings to form DNA molecule. with three A, one C, two G ...
0
votes
1answer
85 views

A point in a circle is selected at random. Calculate probability that point is closer to centre than circumference

State any assumption(s) you make Well, I decided to draw a circle with a center at the origin of a Cartesian plane. It had radius r so it's coordinates on the axes were (0, r), etc. I then drew ...
0
votes
1answer
18 views

On a real line R points a,b are randomly selected such that -2<=a<=2 and 0<=b<=3. Find the probability that | a - b | > 1

Let's say that C is the set where |a-b|>1 So I suppose you could say plot it as coordinates where the x-axis (labelled a) is from [-2,2] and the y-axis (labelled b) is from [0,3]. Now |a-b| must be ...
2
votes
3answers
84 views

In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288

In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288 Please explain how to get this. I understand that we have GGGG => 4 ...
0
votes
0answers
14 views

Question about the poly-Euler preprint

I'm looking over the preprint on poly-Euler numbers, and I think there might be a typographical error on the third line because $j=0$ leads to a discontinuity. Could somebody explain the substation ...
0
votes
3answers
52 views

Count all events for k distinguishable items in n distinguishable bins

I want to count all the possible cases that I can distribute k distinguishable items in n distinguishable bins, for example for 3 items and 2 bins I have the next n^k the possible cases are: I ...
1
vote
1answer
34 views

Set Questions? Need someone to help show

I tried doing these and I have the answers, but I can only do A. Can someone show me how to do the rest? I have the answers but don't know how to get to them..
0
votes
1answer
52 views

A committee requires one accountant, two marketing agents..

A committee requires one accountant, two marketing agents, and four board members. If there are four accountants, three marketing agents, and seven board members available for selection in the ...
0
votes
0answers
25 views

How to measure how many % is done

Let's say that 100 people are going to two exams. They must pass both. In the first exam, 20% of people go forward to the next exam. In the 2nd exam, 50% of people complete and therefore complete the ...
0
votes
0answers
50 views

Possible combination of k unique pairs between two sets

Given two sets $S_1$ and $S_2$, where $|S_1| = n$ and $|S_2| = m$, I want to find all combinations of sampling $k$ unique pairs from the two sets without replacement. How many combinations are there? ...
2
votes
0answers
31 views

Number of elements and number of different basis of $\mathbb F_5^3$

Let $\mathbb F:=\mathbb F_5$ the field with five elements. (i) How many elements has $\mathbb F^3$? (ii) How many different basis has $\mathbb F^3$? My idea: (i) $\mathbb F^3$ has $5^3$ elements. ...
1
vote
3answers
51 views

Proof that the combination formula actually gives you the number of combinations

Ok, there's no problem in defining a binomial coefficient the way it this: $$\binom {a} {b} = \frac{a!}{b!(a-b)!}$$ I can also prove to myself that if I have $n$ elements, like: $\{a_1, a_2, \ldots, ...
-1
votes
3answers
52 views

Show that $C(n,k) = C(n-1,k) + C(n-1,k-1)$ [duplicate]

I'm studying for my final for Statistics, and I want to understand literally every problem in my textbook (at least in the first 7 chapters). One of the problems asks to show that ${n}\choose {k}$ ...
1
vote
1answer
29 views

What's the expected score for guessing on a word bank/“matching” test?

Some quizzes/tests have a "matching" or "word bank" section, which is set up as follows: There are $n$ questions that the student must answer. The answer to each of the $n$ questions is one of $k ...
0
votes
2answers
48 views

Combinatorics question - seats

In how many options can we arrange random number of men (identical men) in line of 15 chairs but: 1. 2 men can't sit next to each other. 2. next to each empty chair - there is at least one men. i ...
1
vote
2answers
67 views

Probability, chose two skittles, out of 2 skittles left from a bag of skittles with 5 colors.

so me and my friend are studying statistics but we are just stuck on this stupid skittle question we made up ourselves when we tried to guess the colors of the two last skittles so we can see who will ...
4
votes
2answers
153 views

Green balls and Red balls, probability problem

I'm studying for my exam and I came across the following draw without replacement problem : ...
1
vote
1answer
43 views

Probability: 30 balls in a bucket, homework

i need some help with some homework, first time i am doing probability and statistics, id like to know if my 2 answers below are correct, and how i can solve the remaining 2. There are 30 balls in a ...
5
votes
6answers
3k views

Fewest number of moves to win the game 2048?

I'm trying to figure out the fewest number of moves one could make to win the game 2048. In another thread, someone placed the figure at 520, but I'm wondering if anyone knows how to mathematically ...
6
votes
3answers
506 views

Why does the keyword “distinct” change the solution to much?

I don't understand why the second answer is different from the first. Aren't they the exact same thing? How many ways can we distribute 10 distinct balls into 5 distinct boxes? $5^{10}$ is correct ...
3
votes
2answers
380 views

What is the probability that $x_1+x_2+…+x_n \le n$?

Given that $X_1, X_2...$ are mutually independent random variables. For each $i$ with $1\le i \le n$ the variable $X_i$ is equal to either $0$ or $n+1$ $E(X_i)$ = $1$ also.. if $X_i$ is equal to ...
2
votes
1answer
83 views

Differentiate $P_{x_n}(z) = \prod_{i=1}^n\frac{1+z+z^2+…+z^{i-1}}{i}$ twice to calculate the variance of involutions.

Use the Probability Generating Function for Involutions: $P_{x_n}(z) = \prod_{i=1}^n\frac{1+z+z^2+...+z^{i-1}}{i}$ To Calculate the Variance of Involutions where: $Variance \space X_n = ...
1
vote
1answer
35 views

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 ...
0
votes
1answer
39 views

probability equiprobable space?

For the problem below are we going to use the equiprobable space. Which is In particular, if S contains n points then the probability of each point is 1/n . For an event A, P(A) = number of elements ...
0
votes
0answers
27 views

2nd Question in introductory probability

There are the same number of red and blue people at a party. And decided to meet up the next day. 1/5 of the red people and 1/3 of all the people were missing. Calculate the probability that a ...
0
votes
1answer
31 views

Beginner question in probability

i'm a beginner in statistics and probability and i need help with a given problem please. We are given a guy who has a machine and a button, the outcames when he presses the button are: a)Music ...
2
votes
1answer
49 views

Probability Question I can't get around.

This is the question from my assignment, which I can't get around. Suppose that a water distribution system is composed of a number of independent pipes. At temperatures below 0 deg C, the pipes ...
0
votes
3answers
485 views

A bowl contains 10 red balls and 10 blue balls, A women selects ball at random without looking?

How can we solve this question ? A bowl contains $10$ red balls and $10$ blue balls, and a women picks up balls from the bowl, at random, without looking. A) How many balls must she pickup in ...
1
vote
2answers
971 views

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 ? ...
0
votes
2answers
31 views

Partioning/Enumeration

How many ways can one distribute A) 15 Balls into 3 bags. Both bag and balls are distinct (labelled) and each bag must contain at least one ball. B) 10 balls into 3 bags. again both bag and balls ...
0
votes
0answers
84 views

Calculate number of combinations & permutations for job assignment to machines

There are 12 machines (M). Each machine can execute for 20 slot (S) of time per session. We have 8 jobs (J) to be done. Each job requires 2 continuous slots (T). There is a fixed timeframe between the ...
2
votes
0answers
65 views

How many different ways can 10 octupuses touch legs?

There are 10 octopuses (octopi?). Each octopus has 8 legs. Legs on an octopus can only touch touch legs on other octupuses. Assuming each leg touches exactly 1 other leg, how many different ...
0
votes
1answer
51 views

Probability that the $9$th extraction is the first one for which $3$ white balls are extracted

We are given an urn with $9$ balls: $5$ black and $4$ white. We extract $3$ balls from this urn at each step, check their colors, then put them back in and repeat. What is the probability that the ...