Combinations are subsets of a given size of a given finite set. All questions for this tag have to directly involve combinations; if instead the question is about binomial coefficients, use that tag.

learn more… | top users | synonyms

0
votes
0answers
10 views

To determine probability distribution for large $N$

To show that the following expression turns to Gaussian for large value of $N$ $$\binom{N}{S}\binom{X}{a}\binom{Y}{b}$$ where $X+Y+S=N$.
2
votes
1answer
27 views

Set of pairs of options that could be wrong/right

One has a list of n options out of which 2 are incorrect, and guesses can be made by picking a pair of options. After picking a pair as a guess, it is either valid, in which case both of the pair's ...
0
votes
4answers
34 views

Combinations and Permutations in coin tossing

I understand the formulae for combinations and permutations and that for the binomial distribution. However, I'm confused about their application to coin tossing. Consider three tosses. Outcomes ...
0
votes
0answers
33 views

Combinations or permutations

I have 3 particles and 5 energy levels (0E,1E,2E,3E,4E). I require all possible ways such that the sum of 3 particles equals 6E. Is there a formula that would enable me to compute the possible ways?
1
vote
1answer
40 views

How many unique ways can I sum $k$ non-negative numbers to $N$?

I have a similar question but not exactly the same as this. I'm trying to determine the number of unique multisets $S\in \mathbb{N}$ that exist when the members are required to sum to a number $N$. ...
-1
votes
2answers
32 views

Combinations and Permutations - tiling a $52\times 3$ grid with $78$ dominos

A grid with $3$ rows and $52$ columns is tiled with $78$ identical $2\cdot1$ dominoes. In how many ways can this be done such that exactly two of the dominoes are vertical. Is this right?- ${78 ...
1
vote
1answer
42 views

The greatest number of points of intersection of n circles and m straight lines is-

The question is about combinatorics. I have no idea on how to start solving the problem. Please guide me. $(a) 2mn+ {m \choose 2}$ $(b) \frac{1}{2}m(m-1)+n(2m+n-1)$ $(c) {m \choose 2}+2({n \choose ...
1
vote
1answer
40 views

Combinations question.

Hi, I have a question to ask regarding subquestion 3. in the picture. I solved it by using ${10 \choose 2}$ since $2$ of the $4$ houses are fixed already, which I thought would leave me with $10$ ...
1
vote
1answer
35 views

2x2 grid game problem

A friend of mine is attempting to make a webpage that has a game for a 2x2 grid that is similar to the old North, South, East, West game. I cannot for the life of me figure this out. Essentially, ...
1
vote
0answers
30 views

Counting problem of combinations of symmetric matrix.

Given, a symmetric $n*n$ matrix $G$ with 0,1 entries. Each row of has same number of 1. $G$ is arranged in a certain order using a rule. The rule is described below- $G$ is partitioned in to two sub ...
1
vote
1answer
38 views

Does every integer occur finitely many times and in what positions in Pascal's triangle?

Given number n, does it occurs finitely many times in Pascal's triangle? In what positions?
2
votes
1answer
31 views

In how many different ways can 3 children share 8 identical sweets so that each child gets at least one?

In how many different ways can $3$ children share $8$ identical sweets so that each child gets at least one? I have tried this problem by listing all the possibilities and I got an answer of $21$. I ...
1
vote
1answer
35 views

Combinations - teachers taking classes

I posted recently trying to work out how many combinations were possible for my scheduling algorithm of teachers to classes. So if I had 4 classes and 3 teachers The combinations would be 4^3 right? ...
0
votes
2answers
14 views

Calculating all Possible Keys vs All possible numbers confusion

With a key of length n bits, there are 2n possible keys. eg: 128-bit key length will have 2128 possible keys But when calculating every possible n digit number, ...
0
votes
2answers
49 views

If $\sum_{k=0}^{n}\binom nk=2^n$ then how is $2(\binom n0+\binom n2+\binom n4+…)=2^n$ [duplicate]

$$\sum_{k=0}^{n}\binom nk=2^n$$ then how is $2(\binom n0+\binom n2+\binom n4+...)=2^n$ ?? I don't think it could be because half of the members of the sum are chosen, that seems a bit intuitively ...
-1
votes
0answers
28 views

Combinatorics: Password consisting of 13 characters. Must contain at least one odd digit, and at most two even digits. How many passwords?

I'm really trying here. I just need help where to go next. Each character is one of the 10 digits 0, 1, 2, ... , 9 What I have so far is that there are 10^13 possible passwords. I'd have to subtract ...
1
vote
1answer
31 views

Number of ways a multiple choice exam can be answered if no two consecutive answers are the same

How many different ways can you answer a 7- question multiple choice exam (with 3 choices) if you know that no two consecutive answers are the same?
2
votes
2answers
58 views

How many sequences of length 6 are formed from the 26 letters without repetition where the first or last letter (possibly both) must not be vowels?

How many sequences of length 6 are formed from the 26 letters without repetition where the first or last letter (possibly both) must not be vowels? I am so lost and confused, but here's my approach: ...
-1
votes
0answers
19 views

Doubt in combination [closed]

The number of distinct combinations, containing at least one $l$ and at least one $i$ of the letters of the word $ illustration $ taken 5 at a time is$\underline{\hspace{1in}}$
0
votes
2answers
20 views

Is there a shortcut to this combination problem?

The question I have encountered is: From 4 oranges, 3 bananas and 2 apples, how many selections of 5 pieces of fruit can be made, taking at least 1 of each kind? So the method I used to solve this ...
0
votes
0answers
19 views

Possible Permutations of Words [on hold]

I have $n$ different words, $k$ zeros, how many possible different strings can they form? For example, I have one word $a$, two $0$, the possible combinations are: $00a,0a0,a00.$ Any number $(\leq ...
4
votes
1answer
44 views

combinations help, 18 boxes, 42 marbles, each box can hold 6 marbles. how many combinations?

I am working on a scheduling algorithm for teachers taking classes, and I am working out possible run times. I have simplified the problem down to this analogy If I had 18 boxes and 42 marbles. Each ...
0
votes
3answers
50 views

How to find every 10 digit number starting from 4?

How many 10 digit numbers are there starting from number 4 There are 1 000 000 000 possible combinations of 10 digit numbers. I want to find out how many of them ...
1
vote
2answers
31 views

Two company and probability example?

I ran into a problem that seems strange to me. Two companies A,B produce a device that with probability $0.05$ and $0.01$ are broken. if we buy two devices produced by one company with equal ...
3
votes
3answers
50 views

Logic behind the combo of cards in a hand that contain only clubs

In looking at a stats problem where you want all combos of a 5-card hand that contain at least one club, the approach I have is to find the combos of 5-card hands that do not contain clubs, and then ...
2
votes
3answers
48 views

Inequality of factorial - Binomial coefficient

my name is Rafał and I decided to create this thread because of my inability to find a solution. I have been fighting with this inequality for 1.5 week and I have a hope that you will give me any hint ...
0
votes
0answers
15 views

Counting permutations of length n without patterns

Count the number of permutations of length n that avoid patterns of high-low-mid. A pattern of hi-lo-mid is 3 integers in the pattern such that for $a_i$,$a_j$,$a_k$, we have i < j < k, $a_i$ > ...
3
votes
1answer
31 views

Combination of $k$ vertices from the $n$ vertices of $n$-sided regular polygon

Select $k$ vertices from the $n$ vertices of an $n$-sided regular polygon. For two of this kind of $k$-combination $A$ and $B$, they are treated as an identical one if $A$ can transform to $B$ by ...
0
votes
1answer
38 views

Three containers first contain $r$ red balls second $g$ green balls and third contains $b$ blue balls

Three containers first contain $r$ red balls second $g$ green balls and third contains $b$ blue balls ..at all I want to draw 3 balls and it doesn't matter from which container .. the problem is to ...
0
votes
1answer
30 views

How to interpret combination and permutation problems?

This is more of a methods question than asking for a specific answer: In revisiting statistics and attempting various problems, I am curious if anyone has any insights on how to "see" the route to ...
1
vote
1answer
40 views

Relationship between Factorial and Binomial coefficients

Over at this link, there is a claim that $(2n)! = n!n! {{2n} \choose {n}}$ - see Tom Boardman's answer, the second one down. I'm wondering why this is the case and if anyone can provide a proof. Is ...
3
votes
3answers
108 views

Find the number of ways to form 15 teams out of 15 men and 15 women.

In how many ways can 15 teams be formed, each consisting of a man and a woman, from 15 men and 15 women. This looks like the same problem as finding the number of bijective functions from a set $A$ ...
0
votes
1answer
17 views

Combinations/probability calculations using ball [closed]

4 balls of different colors with letters A, B , C and D. In how many ways can be placed in a row. If they can be repeated two balls of the same color . How many ways can be located ?
-1
votes
0answers
20 views

How many ways to distribute [closed]

Consider there are 3 books named a, 4 books named b and 7 books named c. In how many ways can we distribute them to a student such that he gets one or more book..?
0
votes
1answer
56 views

Chances of meeting someone in the next 75 years

I have a interesting problem I'm trying to solve. I think you have to use combinations, but I'm not sure. Here's the question: There are only 10 people in the world who are your match. A potential ...
-3
votes
1answer
37 views

Permutation and combination 2 [closed]

In how many ways can5 girls and 3 boys stand in a row so that no one two boys are together. 5 girls can be seated in 5! Ways then the 3 boys can be arranged in remaining 6 place. Which can be done by ...
0
votes
2answers
37 views

Formula to calculate password cracking time in years, taking into account Moore's law and known adversary guessing power [closed]

We know that the biggest human rights violators in human history are capable of one trillion password guesses per second as of approximately January 2013. Assume that the 1 trillion guesses per ...
-2
votes
1answer
32 views

How many combinations can i make using 6 numbers in combinations of 3 [closed]

I have 6 numbers and I'm making groups of 3; and all 3 have to be different, no doubles or triples. how many combinations are possible? Thank you
1
vote
1answer
21 views

Ways of forming a committee

Four couples (husband and wife) decide to form a committee of four members.Find the number of different committees that can be formed in which no couple finds a place is? My attempt:In one case where ...
0
votes
2answers
21 views

No of ways of making a selection.

There are $n$ different books and $p$ copies of each. Find the number of ways in which a selection can be made. My attempt: When he says, make a selection, I assumed that one book is to be ...
1
vote
1answer
38 views

To find number of questions in a test when number of wrong answers is given

In a certain test there are $n$ questions, in this test $2^{n-i}$ students gave wrong answer to at least $i$ questions where $i=1,2,3,\ldots,n$. If the total number of wrong answers given is ...
1
vote
1answer
31 views

Smallest value of n to form 900 n-digit numbers using given digits [closed]

An $n$-digit number is a positive number with exactly n digits. $900$ $n$-digit numbers are to be formed using only $2$, $5$ and $7$. What is the minimum value of $n$ for which this is possible? ...
1
vote
1answer
24 views

Ways of dividing people into groups.

The number of ways of dividing $12$ people into $3$ groups of $4$ each is? My attempt:First we choose $4$ members in $(12C4)$ ways.And then out of remaining $8$ we choose them in $(8C4)$ ways.Finally ...
2
votes
1answer
51 views

indexing all combinations without making list

What is the most efficient way to to find the i'th combination of all combinations without repetition and without first creating all combinations until i. K is fixed (number of elements in each ...
0
votes
0answers
21 views

Permutation and Combination-Number formation with restrictions

How many n-digit numbers exist (digits range from 1 to n) where successive digits of the number are greater than or equal to the previous digit. Digits can be repeated. Please explain the method. ...
0
votes
2answers
18 views

Different Ways to Arrange All Combinations (Without Repeats)

Are there different ways to arrange all combinations without repeats other than the following method. number of items = 6| group size = 4 1,2,3,4 | 1,2,3,5 | 1,2,3,6 1,3,4,5 | 1,3,4,6 1,4,5,6 ...
0
votes
1answer
18 views

Possible Ecommerce Product, Size, and Option combinations

I have an ecommerce site where you can specify the size of a product and any number of options depending on the different products. Each option has a category. For example, for each product you can ...
0
votes
0answers
57 views

Strange Candy Distribution, No two adjacent students get same number of candies.

There are N students and professor has N2 candies. Students get at least 1 and at most N candies and no two adjacent students should get same number of candies. Professor makes the frequency chart for ...
2
votes
5answers
63 views

what is the difference between ${10 \choose 2}$ and ${10 \choose 1}\times{9 \choose 1}$?

I'm not able to understand the difference between these two. Don't both just give the number of ways of selecting $2$ objects from a total of $10$? Maybe the difference is that ${10 \choose 2}$ gives ...
2
votes
0answers
38 views

Representation of positive integers in pascal's triangle [closed]

Prove that every positive integer k, any positive integer n can be written as n = $x_1\choose1$ + $x_2\choose2$ + $x_3\choose3$ ...$x_k\choose k$ eg k=2 n= 5 = $2\choose1$ +$3\choose2$ Is this a ...