1. R

    Combinatorial calculation

    I posted this question in the wrong section, so I post it again here, sorry guys! I'm trying to solve a combinatorial problem, more precisely I have the following data: 1) the Italian car number plates are given starting from 1993 in succession according to this criterion, the first plate...
  2. L

    combinatorial proof

    How can I give combinatorial proof to this ?
  3. L

    Combinatorial proof

    Hi guys any idea how I can give combinatorial proof to the given identities? Thanks in advance.
  4. R

    Error in proof of combinatorial identical equation

    "Concrete Mathematics" second edition equation (5.32) $\sum_{j,k} (-1)^{j+k} \binom{j+k}{k+l} \binom{r}{j} \binom{n}{k} \binom{s+n-j-k}{m-j} = (-1)^l \binom{n+r}{n+l} \binom{s-r}{m-n-l}$ What is the error in the following proof? left $=\sum_{j,k} (-1)^{j+k} \sum_{i} \binom{j}{k+l-i}...
  5. C

    Boolean expression and combinatorial. Need Help...

    Need help to find the boolean expression and combnatorial as per file attached. Thanks
  6. R

    Simple combinatorial designs

    Prove that every (6, 10, 5, 3, 2)-design is simple. A design D is simple if no two blocks are the same. (v,b, r, k, lamda) v, number of treatments or primary factor levels. B, number of blocks K, number of treatments per block. R, number of times each treatment is presented in the design...
  7. R

    Combinatorial Designs and Isomorphism

    Prove that there is a (7, 7, 4, 4, 2)- design and that is is unique up to isomorphism. (v, b, r, k, λ) v, number of treatments or primary factor levels. b, number of blocks k, number of treatments per block. r, number of times each treatment is presented in the design, i.e. the number replica...
  8. R

    Combinatorial Designs: Block Designs

    Suppose D is a block design based on S={1, 2, .., v} with blocks B1, B2, ...Bb. We define a system of distinct representatives (SDR) for D to be a way of selecting a member xi from each block Bi such that x1, x2, ...are all different. If the design D is to have an SDR, it is necessary that D...
  9. C

    Draw two subsets from larger set: Probability of k equal elements?

    Hello, I hope I can get help with the following problem: a) I have a set of natural numbers from 1 to N. I randomly draw N1 of these N numbers (without repetition, order doesnt matter). I randomly draw N2 of these N numbers (without repetition, order doesnt matter). I assume, that both...
  10. J

    Combinatorial algorithm problem .

    Given a matrix A of a regular graph G. The matrix A can be divided into 4 sub matrices based on adjacency of vertex $x \in G$. $ A_x$ is the symmetric matrix of the graph $(G-x)$, where $C$ is the symmetric matrix of the graph created by vertices of $(G-x)$ which are adjacent to $x$ and...
  11. M

    Chess tournament problem. Combinatorial analysis.

    Hi every one. I would like share with you a problem about combinatorial analysis. I can't solve it. In a chess tournament there are n players involved. Assume that every player needs to compete with each of the other players, and assume that there are no ties. how many chess games take...
  12. M

    Combinatorial Hmk

    Hey, I'm taking combinatorics at university in Seoul, Korea. The TA for my class speaks no English so when they do the practice problems I have no idea what the explanation is. I'm a little confused on how to start with these problems and I have no solutions to any of the problems in my book...
  13. M

    Combinatorial problem

    Hi everybody, There are 120 triplets picked out of 10 numbers. 1-2-3,1-2-4,.....8-9-10. What is the minimal number of triplets we can remove from the 120 such as : - no 5-uple could be built using the remaining triplets - only one 5-uple could be built using the remaining triplets -...
  14. F

    Combinatorial problem

    A set has 3^n elements, each of which is either an A or a B. Assume now that this set is divided into three subsets, which in turn is turned into three subsets,etc. At the lowest level, you have sets with three members. Now suppose you have two different decision procedures to determine who...
  15. M

    Combinatorial identities

    Can we express C(n,k) as sum not involving other combinatorials ? Thank you.
  16. P

    A combinatorial problem

    Suppose there are N positions. For each position, one can fill it with S,F or T. There is one constraint that F and T cannot be next to each other. This means that a filling with FT in the sequence or TF in the sequence is not allowed. For example, if N = 5. We have FSSTT, SFSTT are valid...
  17. Q

    Sum of first m terms of a combinatorial number

    Dear My Math Forum denizens, I have a tricky problem that I hope one of you can help me with. (It's for a personal project, nothing to do with school.) I'm looking for a closed-form expression for the sum of the first through m-th terms of a combinatorial number. For those of you unfamiliar...
  18. A

    Help with combinatorial mathematics

    This is from my book on discrete and combinatorial mathematics, in the chapter about combinations (just for clarity, this stuff ). Considering the chapter it is from, simply filling it in shouldn't be the way they expect you to solve it. I probably have...
  19. M

    Combinatorial proof other than strong induction

    Hi guys, I am wondering if there is a way other than strong induction (I already know how to prove it that way for this problem) for this question, " Show that, for any integer n>=4, there exist non-negative integers a,b such that 5n = 10a + 25b" ??? Is there any other way to prove this other...
  20. G

    2 combinatorial probability questions

    I did my entire assignment and these two are driving me nuts. A comittee of fifty politicians is to be chosen from among our one hundred senators. If the selection is done at random, what is the probability that each state will be represented? For this I thought that it should be (50 choose...