# Tagged Questions

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.

31 views

### In how many ways can $5$ students and $3$ teacher sit around a table so that no two teachers are together?

In how many ways can $5$ students and $3$ teacher sit around a table so that no two teachers are together? My attempt: $5$ student can sit $(5-1)!$ in round table. A teacher can sit between ...
28 views

### Infinite Marbles in a Jar with Known Distribution

Let's say I have infinite number of marbles in a jar and $90\%$ of them are red and $10\%$ are green. If I pick $25$ out of the jars (with or without replacement probably doesn't matter because the ...
17 views

### Comparing the task complexity of installing three different offenses for American style football in three days

I want to identify the inherent difficulty of installing three separate American rules football offenses by their complexity of practice schedules in three days then relate those offenses back to one ...
231 views

### How many 6 digit numbers are possible with no digit appearing more than thrice?

How many 6 digit numbers are possible with at most three digits repeated? My attempt: The possibilities are: A)(3,2,1) One set of three repeated digit, another set of two repeated digit and ...
28 views

### the MISSISSIPPI problem - 5 letter word and 6 letter word with constraints

1) Number of ways of selecting 5 letters such that 3 are alike of one type and 2 are alike of another type. There are only 2 ways of selecting 3 letters of the same type i.e., III or SSS. Now with ...
25 views

### Combinatorics [sandwich toppings]

I'm trying to figure out how to solve this excercise; You can order a sandwich from 5 different types of bread, you can have butter, lettuce or neither. You get to choose from 3 types of meat, and ...
26 views

### How do we solve these permutation and combination questions? [on hold]

Q1 In how many ways a panel of six doctors is selected from five surgeons and six physicians if condition is surgeons are more than physicians. A 82 B 81 C 65 D 135 Q2 Find the no. of ...
25 views

### counting the forecasts of 20 chess games

I have a Question... The results of 20 chess games (win, lose, draw) have to be predicted. How many different forecasts can contain exactly 15 correct results? I don't really understand this ...
71 views

### Optimizing Overwatch Team Composition by Player Hero Preference [on hold]

I am wordy by nature - my apologies. My attempt at a TL;DR - I want to design a small tool that optimizes the team composition of a video game based on minimizing the sum of provided player ...
37 views

### calculating probability of a kid have a sister

Suppose there is equal probability of Boy (B) and Girl (G). If a family has 3 kids, wondering what is the probability of a kid has a sister in the same family. I have two methods of calculation, ...
35 views

### Need Help - Plane flight Probability Combinations [on hold]

The flight time of an aircraft depends on its velocity relative to the ground. This speed depends she even own the speed of the aircraft in an inertial frame that moves at speed constant which is the ...
34 views

### Awsome problem of combinations - [on hold]

Among the travelers arriving at Montreal airport to board a plane, (100 * p1)% arrive at destination while the others are in transit. Among those who arrive at their destination, 4% started their ...
37 views

### 100 shoelaces, pick 2 random ends and tie them together, what is the probability that a loop is created?

The question is: There are 100 shoelaces in a box. You pick two random ends and tie them together. Either this results in a longer shoelace (if the two ends came from different pieces), or it ...
30 views

### Any optimized algorithm to find all k values where the sum of k values = S with k>=2 in a defined list [1,2,3,4,…n]? [on hold]

exemple to sole with k=3 list = 1,2,3,4,5,6,7,8,9,10, .. N Sum (S) = 13 Results : [1,2,10],[2,5,6], ..
16 views

40 views

### $48$ balls, draw $6$ balls, how many bets are needed to ensure that exactly $1$ ball matches in at least $1$ bet?

I have a method to calculate it. But it does not make sense. So most likely I misinterpret the numbers. Please show me from where it goes south. The rule This is a simplified version of the lottery ...
33 views

### Permutation and Combination to find pairs

In how many different ways students can be paired such that no pair consists of 2 boys. Given :- Total students = 10, Girls = 7, boys = 3. What my approach is 3 boys can be paired with 7 girls like ...
40 views

### Strong induction postage stamp problem [closed]

Using 5 cent, 11 cent, and 17 cent stamps, what are all possible amounts of postage that can not be formed? Prove your answer. Part of your answer needs to use strong induction.
47 views

### How to use sub-pattern frequencies to calculate the authenticity the main pattern

I'm trying to determine the probability that something is real by comparing the frequency of the sub-permutations it contains. Here is an example: You want to guess whether or not a random symbol is ...
62 views

### Five people have applied for three different positions in a store. In how many ways can the positions be filled?

Five people have applied for three different positions in a store. If each person is qualified for each position, in how many ways can the positions be filled? Can someone tell me if I have to ...
31 views

### Juice problem combinations

I have no idea how to start this question... It's impossible in my mind. Help please The owner of a convenience store reports that 500 people who bought bottled fruit juice in a recent week. 400 ...
29 views

### How to determine a matrix when the sums of rows and columns are given

I was given a $5\times30$ matrix with each element of the matrix can only take 0 or 1. It is given that the sum of each row is 8 and the sum of the first 20 columns equals to 1 while the sum of each ...
### Combinations of up to $n$ out of $m$ elements
Given a set of $m$ unique elements to choose from, and using at most $n$ elements in a combination, how many combinations can I have? A combination can repeat an element more than once, as long as the ...