1. J

    Combinatorics question

    I have a standard deck of 52 cards. How do I find the number of hands of 13 cards that contain 4 cards of the same rank? (A,2-10, J,Q,K) I'm starting off with (48 choose 9) but I am unsure of how to account for the multiples that have been calculated (the Inclusion, Exclusion principles)...
  2. P

    Combinatorics: Word Arrangement Problem

    A screenshot to my problem: I found a Chegg answer to the word WISCONSIN, and I understand that you separate each letter into its appearance but afterwards they didn't really explain much about how to solve it. They just solved it with no explanation and I can't...
  3. P

    Combinatorics Question

    I'm having issue solving this problem If they were said that xi are non-negative integers I would know how to solve it. It would be n = 32, k = 6, and then (32+6-1) chooses (6-1). But I'm not sure how to apply any of these constraints. My professor didn't go into detail about it and only...
  4. M

    Combinatorics. What is this called?

    Hi. I hope this is the right forum. Here's what I did: I took all the permutations of 1234 and arranged them based on how much the digits of any group of permutations are spread out. In every group, the next permutation is obtained by increasing every digit of the previous one by 1 (4 loops...
  5. O

    Combinatorics with several conditions

    Hello. I have a math problem that I need to solve, however Im really stuck and also kind of depressed now. We have 30 balls. 6 red, 7 white, 9 green and 8 blue. We want to seperate them to 4 different boxes. · First box can only contain 13 or less balls, which can be either red or...
  6. Vinod

    Combinatorics problem

    In how many ways can two rooks of different colours be put on a chessboard so that they can take each other?(Thinking)
  7. P

    No. of ways to divide 6 pairs into 3 teams so that no pairs are in the same team

    There are 6 pairs (12 people) and they must be divided into 3 teams. All teams must have 1 or more occupants. Both people from a pair must not be in the same team. I already answered a similar question, the only difference was that there were two teams instead of three. If x is the number of...
  8. L


    What is the counting logic behind this question?
  9. H

    Topics for a research paper that is not yet studied/discussed

    I am a college student taking up a Mathematics course. Our field only accept the topics about number theory/combinatorics/graph theory/algebra/mathematics. But I don’t know what topic I should use. I’ve been rejected many times by our professor. I'm running out of ideas. A topic with an...
  10. A

    a simple combinatorics (i assume) problem

    I feel that kind of problem should be very easy, but still got no clue how to solve it.(Thinking) Cars have 4 wheels, trikes - 3 wheels, trucks - 6 wheels. What's the number of all possible vehicle combinations that have a total amount of wheels of 50. Thanks.
  11. C

    Deduce formula for $\sum_{j=0}^m {m \choose j}(-1)^j j^{m+1} $

    I am working on the following problem: For each $m$ we have found the values of $$\sum_{j=0}^m {m \choose j}(-1)^j p(j)$$ for polynomials of degree at most m. Use a combinatorial story to find the Stirling number $$m+1 \brace m$$ and deduce a formula for $$\sum_{j=0}^m {m \choose j}(-1)^j...
  12. TriForce

    Combinatorics problem

    Problem: 15 books should be divided between two bookshelves, each shelf should at least have one book. In how many ways could this be done? I think I've solved the problem, but It's an ugly solution based on brute force observation and not really comprehension. So I realized that if you take...
  13. L

    Combinatorics optimization case

    I hope im posting this in the right place, I don't know under which category combinatorics goes. Anyway: If we have Y number of categories of building blocks. Each category has X number of variants. Each variant is associated with a unique cost. One variant from each category is put...
  14. S

    Combinatorics Problems solved by Pascal in 1654

    Players A and B play a sequence of games. The first one to win 10 games is the overall winner. A won 8 games so far B won 7 games so far. Assuming that each player wins a game independent of previous outcomes with probability 1/2, what is the probabilty of each player becoming the overall...
  15. S

    Combinatorics Matching Problem

    There are n different elements randomly assigned to n different spots. There is exactly one "correct" spot for each element. What is the probability that at least one element is assigned to its "correct" spot? My idea was: $1-P(\text{No element is assigned to its correct...
  16. S

    Combinatorics question

    Hello, thank you in advance for help here. I am just trying to figure this out for my own edification. If I took 6 dice, each a regular 6 sided cube, how many possibilities are there of me rolling a four of a kind and a two of a kind? In other words, rolling a 646646, 222112, 333344, any abaaba...
  17. C

    Combinatorics problem

    You guys dont have Combinatorics subforum so i'm just gonna put this here. I found some random book on the internet and there was one problem, it goes like this "How many different necklaces of six beads can be formed using three reds, twoblues and one green?" Here is an example of what some...
  18. F

    Solving a circular permutation related problems

    N people are invited to a dinner party and they are sitting on a round table. Each person is sitting on a chair there are exactly N chairs. So each person has exactly two neighboring chairs, one on the left and the other on the right. The host decides to shuffle the sitting arrangements. A...
  19. F

    horse race counting

    In a race there are n horses.In that race, more than one horse may get the same position. For example, 2 horses can finish in 3 ways. Both first horse1 first and horse2 second horse2 first and horse1 second How can I find out the number of ways the race can finish for any n.Is there any...
  20. C

    Combinatorics: License Plate

    Digits include 0, 1, 2, ..., 9. How many license plates can be made out of 3 letters and 3 digits if the first and the last symbol must be a digit? These are my thoughts: At the first and last positions we must have a digit, so there are 10 possibilities in each of those slots. For the...