# combinatorial

1. ### 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. ### combinatorial proof

How can I give combinatorial proof to this ?
3. ### Combinatorial proof

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

11. ### 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. ### 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. ### 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. ### 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. ### Combinatorial identities

Can we express C(n,k) as sum not involving other combinatorials ? Thank you.
16. ### 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. ### 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. ### Help with combinatorial mathematics

This is from my book on discrete and combinatorial mathematics, in the chapter about combinations (just for clarity, this stuff http://en.wikipedia.org/wiki/Combination ). 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. ### 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. ### 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...