0
votes
1answer
5 views

How many base-out configurations would be possible in sleazeball?

Problem: In a baseball there are 24 different "base out" configurations (runner on first - two outs, bases loaded- none out, and so on). Suppose that a new game, sleazeball, is played where there are ...
1
vote
2answers
32 views

How many ways can SLUMGUILLION be arranged so all three L's precede all other consonants?

How many ways can the letters in the word SLUMGULLION be arranged so that the three L's precede all the other consonants. Attempt: There are 11 letters, and there are 3 Ls, 4 vowels: U U I O, and 4 ...
0
votes
2answers
35 views

How many hamburgers can be ordered, if there can be eight toppings?

A fast food restaurant offers customer a choice of eight toppings that can be added to a hamburger. How many different hamburgers can be ordered? Attempt: I don't know if this is correct 8!? I think ...
0
votes
1answer
17 views

How many straight lines can be drawn between five points (A, B, C, D, and E), no three of which are colinear?

How many straight lines can be drawn between five points (A, B, C, D, and E), no three of which are colinear? Attempt: Given 5 points, a line consist always of 2 points. Thus the total number of ...
2
votes
2answers
39 views

Expected number of people getting their own hat given that at least one of them gets his hat.

Suppose there are $N$ people at a party. Their hats get mixed and when leaving they grab a hat at random. Let $\displaystyle X_i=I(\text{$i$th person gets his own hat})$ and ...
0
votes
1answer
20 views

How many zip codes are as large as 6000-0000, are even numbers, and have a 7 as their third digit?

When they were first introduced, postal zip codes were five digit numbers, theoretically ranging from $00000$ to $99999$. (In reality, the lowest zip code was $00601$ for San Juan, Puerto Rico; the ...
0
votes
3answers
29 views

In how many ways can the word ELEEMOSYNARY be arranged.

In how many ways can be the letters of the word ELEEMOSYNARY be arranged so that the S is always immediately followed by a Y? Attempt: There are 3 Es, and 2 Ys, and and then all letters appear once ...
0
votes
1answer
17 views

Using the Total Probability Rule

From one box with 6 white balls and 4 red balls, we pick out without replace 4 balls randomly and are transfered to another box which is initially empty. From this second box, after, are selected 2 ...
2
votes
1answer
21 views

How do I find the PMF of X when X is the number of flips of a fair coin that are required to observe the same face on consecutive flips?

How do I find the PMF of $X$ when $X$ equals number of flips of a fair coin that are required to observe the same face on consecutive flips? The hint was to draw some sort of a tree diagram, but I'm ...
1
vote
1answer
20 views

Distinct elements in the Union and Intersection of A and B

Take a set $x$ with $10$ distinct elements. Rule: Everytime you have two subsets, $A$ and $B,$ you also have $A\cup B$ and $A \cap B.$ What is the maximum number of subsets you can have such ...
1
vote
1answer
12 views

How many different eight note melodies within a single octave can be written if black/white keys alternate.

An octave contains 12 distinct notes(on a piano, five black keys and seven white keys). How many different eight notes melodies within a single octave can be written if the black keys and white keys ...
0
votes
2answers
20 views

A coke hand in bridge from deck of cards.

A coke hand in bridge is one where none of the thirteen cards is an an ace or is higher than a 9. What is the probability of being dealt such a hand? Attempt: Suppose the thirteens cards are amoung ...
0
votes
1answer
33 views

Five cards selected out of 52 cards. Find probalbilty sum of the faces is 48 or more.

Five cards are dealt from a standard 52 card deck. What is the probability that the sum of the faces on the five cards is 48 or more? Attempt: Five cards can be selected out of 52 cards by 52_C_5 ...
1
vote
1answer
39 views

What are chances that not all S's will be adjacent given a phrase at random.

IF the letters in the phrase A ROLLING STONE GATHERS NO MOSS are arranged at random, what are the chances that not all the S's will be adjacent. Attempt: Given there are 6 letters that appear twice, ...
0
votes
3answers
21 views

Combinatorics/probability dinner party type problem

At a banquet, 9 women and 6 men are to be seated in a row of 15 chairs. If the entire seating arrangement is to be chosen at random, what is the probability that all of the men will be seated next to ...
0
votes
2answers
22 views

Lottery problem - Chance of 4 out of 5 balls matching?

In a lottery, an urn contains 40 balls that are numbered 1, 2, ..., 40. Each week, 5 balls are drawn from the urn without replacement. To enter, one chooses 5 numbers. Anyone who correctly predicts ...
1
vote
1answer
27 views

A bridge hand (13 cards) is dealt from a standard 52 card deck. Given events A and B, find $P(A \cup B)$.

A bridge hand (13 cards) is dealt from a standard 52 card deck. Let A be the event that the hand contains four aces. Let B be the event that the hand contains four kings. Find $P(A \cup B)$. Attempt: ...
0
votes
0answers
23 views

Suppose that we have 4 white and 7 black balls - Probability Question [on hold]

Suppose that we have 4 white and 7 black balls in a bowl, and randomly select three of the balls. We are interested in knowing the probability that one of the balls is black and the other two white. ...
1
vote
1answer
52 views

How many ways different sets of values can be chosen for the $x_s$ , if $x_1 + x_2 + x_3 = 20$?

Your statistics teacher announces a twenty-page reading assignment on Monday that is to be finished by Thursday morning. You intend to read the first $x_1$ pages Monday, the next $x_2$ pages ...
0
votes
1answer
38 views

How many ways can a twelve member cheerleading be pair up.

Problem: How many ways can a twelve member cheerleading squad(6 men and 6 women) pair up to form 6 male-female teams? What might the number 6!6!2^6 represent? What might the number 6!6!2^6*2^12 ...
2
votes
1answer
32 views

Forming a sequence from a given set

28 random draws are made from the set {1,2,3,4,5,6,7,8,9,A,B,C,D,J,K,L,U,X,Y,Z} containing 20 elements. In each draw, one element from the set is drawn with replacement. What is the probability that ...
1
vote
1answer
34 views

How many dice do you have to roll to get your odds of seeing each face at least once equal to 0.5?

In a pub the owner is throwing a number of dice simultaneously. "I am trying to get one of each of the six faces", he says, "But it hasn't happened yet". "No", I said "You need at least four more dice ...
1
vote
1answer
29 views

Random distribution of colored balls into boxes.

This is an abstraction of a real problem I have: I have a large number of balls that are either Red or Blue ($n = 9*10^7$) and a bunch of containers ($c = 3*10^7$). I've calculated that the ...
1
vote
1answer
10 views

Expected Homogenization Time

Assume we have $N$ boxes, and each box contains one red sock and one blue sock. We can then perform the following process: randomly take one sock from each box and replace it with a red sock. What is ...
1
vote
2answers
73 views

multiplication rule questions - 7 people attending a concert

7 people are attending a concert. (a) In how many different ways can they be seated in a row? (b) Two attendees are Alice and Bob. What is the probability that Alice sits next to Bob? (c) Bob ...
0
votes
0answers
28 views

Probability of a number of weighted items being allocated to the same bin

I have the following (probably classic) combinatorics problem: There are $n$ bins that can hold $k$ items each, and a total of $r = n\,k$ items. The items have weights $w_1 > w_2 > \dots ...
1
vote
1answer
28 views

Probability theory problem , inequality

Let $n$ be a positive integer and $a , b$ two randomly chosen positive integers not exceeding $n$. Let $P(n)$ denote the probability that $\begin{equation} \\ a ^ 2 + b ^ 2\leq n^2 \end{equation}$. ...
0
votes
2answers
20 views

Amount of ways to schedule activities using combination or permutation.

I'm trying to review for Probabilities and Statistics and came upon this Question. If one needs to schedule a job interview for someone who wants to teach at a school. For the day of the interview, I ...
1
vote
1answer
21 views

Reversing Combinations to find probabbilities of variable two state systems

First I'm going to lay out the problem and do an insanity check to make sure I've planned out properly so far. The first question is probably trivial, but the second one is definitely a bit more ...
3
votes
0answers
40 views

On a problem of sphere-packing for Reed-Solomon codes

Suppose we have an $[n, k+1, n-k]$ Reed Solomon code $\mathcal C$ over $\mathbb F_q$, where $n-k=d$ is the minimum distance, and suppose that $d=2t+1$. We know that for every $r \in \mathbb F_q^n$ the ...
0
votes
1answer
48 views

A question on Probability / Combinatorics [closed]

Three People each write down numbers 1..10 in a random order. What is the probability that all 3 people all have at least one number in the same position ?
0
votes
3answers
45 views

Box containing Red and black balls

A box containing 4 red balls and 6 black balls . Three balls are selected randomly from the box one after the another, without replacement . The probality that the selected set has one red ball and ...
1
vote
1answer
30 views

Number of ways of distributing 7 distinct balls into 7 distinct boxes with exactly one box with 3 balls.

This is what I tried. I can distribute the balls in four ways: 1) 3,1,1,1,1 2) 3,2,1,1 3) 3,2,2 4) 3,4 For 1) I can first pick 5 boxes in ${7 \choose 5}$ ways and then pick 3 balls in ${7 \choose ...
0
votes
0answers
42 views

How many Possible Combinations exist?

I have $120$ coins and $21$ buckets. Each bucket can hold $0$ to $20$ coins. How many possible coin/bucket combinations are there?
0
votes
1answer
46 views

Calculating partitions using multiplication rule

A teacher wants to create 4 study groups of 5 students from a class of 20 students. How many ways are there to do this? The answer is $\binom{20}{5}\binom{15}{5}\binom{10}{5}\binom{5}{5}$. I don't ...
2
votes
1answer
163 views

Probability that the second-best player finishes second in a single-elimination tournament, given that better players always defeat weaker players?

A chess tournament (single-elimination format) has 16 players. Suppose that no two players have the same strength, and that each player always defeats the players weaker than himself/herself (i.e. no ...
0
votes
1answer
19 views

Probability that a company is worth $xM after y years, if its value can only stay the same or double every year?

Let's say a company is worth \$1M. Each year, the value of the company eithers stays the same with probability $\frac{1}{2}$, or doubles with probability $\frac{1}{2}$. What is the probability that ...
1
vote
4answers
76 views

Probability of at least 3 red balls given 4 choices in a bag of 4 red balls and 4 black balls?

Let's say there are 8 balls in a bag, where 4 are red and 4 are black. If I choose four balls from the bag without replacement, what is the probability that I will choose at least 3 red balls? My ...
1
vote
2answers
31 views

Probability of being selected twice in a week given a set of n people?

Let's say a child is selected out of a group of 10 students each day to stay after school and help clean the classroom. What is the probability that a particular child is selected exactly twice during ...
1
vote
2answers
19 views

K Zeros between 14641

One Writes K- Zeros between every two digits of the number 14641. What is the square root of the number obtained? I want to know if there is a better way of writing out the solution. As of now I know ...
0
votes
1answer
27 views

Find probability of 4th smallest number?

Seven numbers are selected from the numbers (1, 2, 4, 8, 9, 10, 11, 15, 17) without replacement. What is the probability that the 4th smallest number is 9? I'm not sure if I'm getting the correct ...
0
votes
4answers
47 views

How many 3 digit even numbers can be formed using (0, 1, 2, 3, 4) and no repetition?

My solution to the problem is as follows: The answer I get is 27. My reasoning is that the last digit must be even, so for that position there are 3 choose 1 possibilities. Then the first digit ...
1
vote
2answers
101 views

Grid problem - combinatorics? [closed]

In a city, streets are laid out as a grid. Your home is at location (0,0) and work is at location (10,10). You walk to work taking only steps up and to the right. (a) How many distinct ways can you ...
1
vote
1answer
22 views

Number of outcomes times probability of failure is number of failures?

I was hoping someone could spread some insight on why this is true? Suppose that in some situation, there are n! number of possible outcomes. Also, suppose that p is the probability of failure of ...
0
votes
1answer
38 views

Even product on 5 dice rolls

A fair die (d6) is thrown five times. What is the probability that the product of the five scores is even? I have tried the following approaches. The first seems unnecessarily complex and also wrong: ...
0
votes
1answer
18 views

Combinatorics Forming a word from set of Alphaphets

A sequence of 15 random draws, one at a time with replacement, is made from the set { A,B,C ...,X,Y,Z } of the English Alphabet(26 Alphabets in total). What is the probability that the string ...
0
votes
0answers
42 views

Dependent Expectation in Random Numbers Illustrated by Prime Repetition in Pi

When approximating Pi, appending each numerical digit as you refine, what is the first repetition of a four-digit prime number? For instance the first repetition of any one-digit number in the ...
0
votes
1answer
31 views

Ordered sequences of integer with fixed sum

Let $I_S = \{0, 1, \ldots, S\}$, with $S \geq 1$. Consider all the ordered sequences of length $L \geq 2$ in $I_S^L$ such that the sum of all the terms is equal to $S$. Let $N(L,S)$ be the number of ...
3
votes
1answer
81 views

Probability of at least m in a row out of n? (generic formula)

In a previously asked question of mine, I was specific in asking for a 75% freethrow shooter, what is the probability he would make at least 5 freethrow shots in a row out of 10. That means he would ...
2
votes
2answers
106 views

Combinatorics of a tournament where one wins by taking either three games in a row or four in total

Two teams play each other repeatedly until either one of them wins three games in a row or one of them wins a total of four games. What are all the ways in which the tournament can be played? What ...