Tagged Questions
0
votes
0answers
26 views
Calculating the probabilities of different lengths of repetitions of numbers of length 6
This question is similar to the question I asked here: Calculating the probabilities of different lengths of repetitions of numbers of length 4
except now I'm having problem with numbers of length 6.
...
0
votes
1answer
24 views
Combination of arrangement and probability
Four guys and four girls are arranged in a row such that no two girls are together. What is the probability that any two of the four guys are together?
2
votes
6answers
51 views
calculate the number of possible number of words
If one word can be at most 63 characters long. It can be combination of :
letters from a to z
numbers from 0 to 9
hyphen - but only if not in the first or the last character of the word
I'm trying ...
1
vote
2answers
32 views
Number of length-five words
How many length-five words can be written using two A's, two T's and one E?
Why is it not $\binom5 2 \times\binom 5 2 \times \binom 5 1$?
Is it $ \binom 5 3 = 10$?
1
vote
1answer
23 views
Dice Roll Permutation Problem
Here is my problem:
You have a standard dice, with possible rolls: $\{1, 2, 3, 4, 5, 6\}$. How many permutations exist in 10 rolls such that no two immediate rolls are the same?
For example:
$\{1, ...
1
vote
1answer
58 views
Permutation & Combination - how many numbers smaller than $2.10^8$ and are divisible by $3$ can be written by means of the digits $0$,$1$ and $2$
How many numbers smaller than $2.10^8$ and divisible by $3$ can be written by means of the digits $0$,$1$ and $2$?
Left Zero padding not allowed.
I am getting this as -
3 digits - 2*3 = 6
4 digits - ...
2
votes
2answers
58 views
At least two people have the same birthday
If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday?
I tried solving ...
2
votes
2answers
30 views
Variance of derangements
Suppose I choose a random permutation on n numbers. It is easy to prove that the mean of the number of fixed points (i.e. the numbers that get mapped to themselves) is 1. Is there an easy (constant) ...
0
votes
2answers
36 views
How to count permutations with restrictions on how items are grouped
I am trying to solve the following problem:
A town contains $4$ people who repair televisions. If $4$ sets break down, what is the probability that exactly $i$ of the repairers are called? Solve ...
0
votes
1answer
15 views
Probability of a subset occuring within a section of a permutation
I have a list of permutations of a vector of length 24. In each position of the vector is a number between 1 and 24 and repeats are not allowed.
An online tool tells me that this will give ...
2
votes
1answer
48 views
Any comprehensive material to revise the mathematics
I left school long back and so my mathematics knowledge also fades out.
I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations.
I tried ...
0
votes
1answer
34 views
The letters A, E, I, P, Q, and R are arranged in a circle. Find the probability that at least 2 vowels are next to one another
This isn't homework, but could someone please give an explanation and answer to this question. Thanks! :D
0
votes
2answers
64 views
The letters A, E, I, P, Q, and R are arranged in a circle. Find the probability that at least 2 vowels are next to one another.
I've had trouble for his one for a while now. All help would be greatly appreciated.
My attempt:
Alright, since one letter is fixed, that leaves us with 5 letters to arrange. I'm going to fix the ...
2
votes
2answers
39 views
number of ways poker card question
I am having difficulties to calculate the number of ways 11 poker card can be chosen such that two cards of one suit, two cards of another suit, four cards of another suit, three cards of another ...
0
votes
1answer
43 views
Is there a known distribution for this permutation with replacement problem? [duplicate]
Choose $t$ numbers from $n$ $(n>t)$ distinct numbers with replacement and the order of the $t$ numbers matters.
Say,
$P(X=1) = \dfrac{{numbers\ of\ unique\ t-set \ which\ has\ 1\ distinct\ ...
0
votes
1answer
128 views
how many permutations can a 18 digit number have?
How can I work out how many permutations a 18 digit number may have that using digits 0-9?
I found this (How many permutations are there if you have n+1 items, where the extra item can be repeated?) ...
1
vote
2answers
85 views
probability and combinations
I have just started probablity and I am trying to understand these question.
A study has found that 60% of all companies say that the cost of health care is too high.
If we choose 8 companies at ...
0
votes
2answers
78 views
A probability problem - probability of one card being red and the other one being black.
Consider a deck of 50 playing cards (2 cards missing). What is the probability that one of them is red and the other one is black? I've got two solutions which one is correct ?
Let $R$ represent red ...
1
vote
2answers
293 views
Combinatorics and Probability Problem
The problem I am working on is:
An ATM personal identification number (PIN) consists of four digits, each a 0, 1, 2, . . . 8, or 9, in succession.
a.How many different possible PINs are there if ...
0
votes
1answer
37 views
Probability of A Specific Type of Experiment Occuring
The problem is:
An experimenter is studying the effects of temperature, pres-sure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different ...
1
vote
1answer
28 views
In how many ways can 2 motors and 2 switches be selected?
I'm not sure if order matters in this question. I believe that order matters the way that it is worded with selected, but any insight would help with the question below:
The supply department has 8 ...
3
votes
1answer
51 views
I don't think I'm doing this function mapping question correctly, could anyone offer advice?
We were given the following question in class:
...
1
vote
2answers
44 views
How would I determine the number of solutions for the sum of this number?
We're given the following equation:
$$x_1 + x_2 + x_3 + x_4 + x_5 = 20$$
I know that the simple amount of solutions to this is $\binom{5+20-1}{5-1}$, but for the following questions I'm slightly ...
1
vote
1answer
30 views
How would I go about solving this statistics question on permutations?
Columba has two dozen each of n different coloured beads. If she can
select 20 beads (with repetition of colors allowed) in 230,230 ways,
what is the value of n?
I'm trying to figure it out, ...
1
vote
1answer
86 views
How many combinations are possible keeping the sum constant
How many combinations of numbers are possible keeping the sum of its digits as a constant. My problem is like this :-
How many numbers are possible keeping the sum = 9 between 9 and 9000 ? ie,
...
1
vote
1answer
86 views
0
votes
1answer
54 views
Simple question about combinations
There is this problem I found in a book on combinations. It goes roughly like this:
There are 4 type A machines and 5 type B machines. Three of the machines are removed from the piles. What is the ...
2
votes
1answer
129 views
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
The toys are differnt here but the boxees are identical.
since no box can be empty we can have two situations for this.
...
0
votes
1answer
58 views
Worst case probability of a point on 2 circles lining up.
Imagine 2 circles connected at 1 point. The smaller of the circles has n equally spaced points around its perimeter labelled $1...n$. The larger of the circles has $n^2$ equally spaced points around ...
1
vote
1answer
86 views
Password Permutations
Could somebody answer me how many possibilities are there for a six-letter (only letters, but case-sensitive) computer password?
Is it $^{52}C_6 \times 6!$ ?
1
vote
0answers
97 views
Card game-ordering a deck [duplicate]
Possible Duplicate:
Game Theory Matching a Deck of Cards
Suppose we take a blank deck of $52$ cards, write the number $1$ on the first card, $2$ on the second card, and so on until we write ...
0
votes
2answers
213 views
Find the number of circular 3-permutations of 5 people?
Find the number of circular $3$-permutations of $5$ people?
Please correct me if I'm wrong:
$C(5-1,3)=4$
1
vote
1answer
117 views
Combination , finding number of cases
How many strings with five or more characters can be formed from the letters SEERESS?
Correct me Please,
This is my answer for $6$ characters :
$\frac{6!}{3!\cdot3!} = 20$
$\frac{6!}{3!\cdot2!} = ...
1
vote
0answers
42 views
secretary hiring algorithm
So I have to figure out that in the case of the secretary problem(http://en.wikipedia.org/wiki/Secretary_problem) what is the probability that I hire exactly one applicant over the course of going ...
5
votes
1answer
97 views
Combinatorial properties of permutation groups
Let $P_n$ denote the set of pairs $(x,y)$ of permutations on $S_{2n}$, where each permutation is a product of $n$ disjoint cycles of length two. Let i and j be two fixed elements of the set $\{1,2, ...
0
votes
3answers
122 views
Probability of winning a pick 3 lotto game?
If you are given 3 standard 6-sided dice, and are asked to pick the order of the numbers that will appear; what is the probability that you will win, given that order DOES matter?
1
vote
3answers
67 views
Prove that $n!e-2$ $<$ $\displaystyle \sum_{k=1}^{n}(^{n}\textrm{P}_{k})$ $\leq$ $n!e-1$
Prove that $n!e-2$ $<$ $\sum_{k=1}^{n}(^{n}\textrm{P}_{k})$ $\leq$ $n!e-1$ where $^{n}\textrm{P}_k = n(n-1)\cdots(n-k+1)$ is the number of permutations of $k$ distinct objects from $n$ distinct ...
1
vote
2answers
67 views
Number of Sets problem
A class is attended by $n$ sophomores, $n$ juniors, and $n$ seniors. In how many
ways can these students form $n$ sets of three people each if each set is to contain a
sophomore, a junior, and a ...
1
vote
2answers
118 views
How many ways he can attempt the paper?
Joey has to attempt a question paper that has 3 sections with 6 questions in each section .
If he has to attempt any 8 questions , choosing atleast 2 questions from each section.
Then in how many ...
0
votes
1answer
426 views
Distribute distinct objects in identical boxes
Number of ways to distribute 6 Distinct objects to 3 Identical Boxes such that each should have atleast one?
Is there any standard formula for these sums,
as we have for identical - different pair ...
1
vote
2answers
399 views
How to calculate the expected frequency of a pattern?
I'm working on a problem to find the expected frequency of a pattern.
Say there is a sequence of alphabets - A, B, C and D.
The sequence is:
ABDACDBADA.
I want to find the expected frequency of a ...
1
vote
3answers
189 views
Ways of selecting at least one man
We have to select a group of 7 out of a group of 9 men and 11 women
Q : How many seven member teams consist of at least one man ?
Now I know that the answer is ${20 \choose 7}-{11 \choose 7} ...
3
votes
2answers
157 views
odds of picking exactly 2 women and 2 men out of 12 men and 12 womem
I understand the answer to be 12 choose 2 * 12 choose 2 over 24 choose 4.
I don't really understand why, or what principle I can extract from the problem. I can understand that we are putting the ...
4
votes
1answer
264 views
question involving Markov chain
Let $S_{2m}$ be the group of all permutations $\pi$ of $\{1, 2, \ldots, 2m\}$. The following transition kernel $S$ generates the random transposition walk
$$
Ch(\pi, \pi')= \begin{cases}
\frac{1}{2m} ...
1
vote
1answer
77 views
Solving this permutation
I know this is an extremely noob question, but I need some help. since I am stuck
Prove the formula
$$p(n,r) = \frac{(n + 1 -r) \; (r^2 - 3r + 3) \; (r-2)!}{n!}$$
from this answer.
0
votes
0answers
54 views
$i$ balls to paint $k$ colors, and exactly $k' < k$ colors should be used. How many ways to paint?
Another ball-painting problem: assume that we have $i$ balls (with numbered labels, so order is sensitive), and $k$ different colors. Now we need to paint these balls using these colors so that ...
0
votes
2answers
98 views
Probability of random shuffling of cards
I have a pack of cards and use the following method to shuffle them
Pick a random card from the deck and replace the first card with it
Put the first card back in the deck
Move to the second card ...
1
vote
0answers
74 views
Random Permutation Poisson proof
Let $F$ be the number of fixed points of a random permutation on $n$ items. Show that as $n$ approaches infinity, the distribution of $F$ approaches a Poisson distribution with a mean $(\lambda)=1$.
0
votes
1answer
232 views
Random permutation problem
Let $\pi$ be a random permutation of $n$ objects and let $ T := \text{the number of transpositions in } \pi $. Use Chebychev's Inequality to find an upper bound for $T\geqslant k$.
Okay the problem ...
2
votes
1answer
149 views
Simple Dice Rolling Problem
If you play poker dice by simultaneously rolling 5 dice, why is $P\text{{five alike}} =.0008$?
I guess I understand the fact that each dice has the probability to land on the same number $1/6$ of the ...
