Combinatorics Definition and 421 Threads

Hey guys, I have a few questions: 1. There are 35 desks in a classroom. In how many ways can the teacher configure a seating plan for a class of 30 students? I'm not sure if order matters (35P30 or 35C30). 2. Sixteen people attend a meeting. Each person greets everyone with a single...

I've just managed to stump myself. Let's say you have M (identical) marbles and N boxes. How many ways can you put the marbles in the boxes if each box can have at most k (k <= M) marbles? for k=M we can take M .'s to be the marbles and N-1 |'s to be the boxes so a valid configuration...

Hey, so in 2003, it was announced that the human genome was more or less mapped. The difference between individual humans is about 0.2 percent of the 3 000 000 000 genes we have. So somehow, this percentage should account for all of the human variations that aren't dependent on environment...

Suppose you want to assign seats for a single row of 4 guys and 4 girls in such a way that each guy is sitting next to at least one girl and vice versa. How many ways are there to do this? This is not a hard problem at all, but I am lacking a good outlined approach to solving problems of this...

Can anyone help with this proof? Let k be an element of positive integers. prove that there exists a positive integer n such that k|n and the only digits in n are 0's and 3's This is in section on the pigeon hole principle and the only problem I have left. I'm not really sure where to...

Hi. We are doing permutations and combinations in class and we were given some formulas without proof to remember. I was able to derive most of them but was unable to derive 3 of them. But I would like to see how do I derive them for sake of fun (also if I forget them what will I do. :) ). 1...

Combinatorics...evil problem! Hi all, I am working on my combinatorics homework. I have completed all of the problems but one. Here it goes: ------------------------------------------ Let S_1 and S_2 be two sets where |S_1| = m and |S_2| = r, for m,r in Z+ (positive integers), and the...

We were given an extra credit problem in discrete structures 2 today. The problem is: n people go to a party and leave a hat. When they leave they take a random hat. What is the probability that no one ends up with the same hat? I can calculate the probability, but I was just wondering if I can...

There are 6 tennis players and each week for a month (4 weeks) a different pair of 5 play a tennis match. How many ways are there to form the sequence of 4 matches so that every player plays at least once? I believe this is an OR problem, but I don't know how to handle the 4 weeks information...

hey guys I am taking a class right now called Finite Mathematical Structures, and I am having a pretty tough time. although it's only about 1 - 2 weeks into the semester, i am having a hard time actually understanding graph theory problems. so far we are doing isomorphisms, edge coverings...

The question goes something like this... What is the probability of an E being one of the 4 randomly chosen letters from the word ENERGISE? This is how i did it (the book says its wrong): ENERGISE ==> 3 Es, 5 Non-Es (partitioning) hence: (3c1*5c3)/(8c4) the book has 55/56...

Birthday Problem (need help on combinatorics...) URGENT! Question: There are ''n'' ppl in a room. What's the probability of 2 or more ppl sharing the same birthday? My Answer: (Looking at 2 ways...) Let E be Event of 2 or more ppl sharing the same birthday... then: P(E) = 1 - P(E')...

Given a Natural number K, how many combinations \[ x = \left( {x_1 ,...,x_N } \right) \] of Natural numbers vectors are there, so that \[ \sum\limits_{i = 1}^N {x_i ^2 } = K \] ? I'm desparate and will believe anything...

Suppose you play a game of cards in which only four cards are dealt from a standard deck of 52 cards. How many ways are there to obtain three of a kind? (3 cards of the same rank and 1 card of a different rank, for example 3 tens and 1 queen.) Could someone help me with how to do this...

Here's a problem my friend gave me: The number of points of intersection of diagonals of a n-gon is 70. If no three diagonals are concurrent, find the number of sides of the n-gon. I believe the answer is 20. I tried to work out for small values of n to get a feel but that didn't do...

:zzz: :zzz: :zzz:

Hello all In my calculus book, this problem has been pestering me" Prove nC(k-1) + nCk = (n+1)Ck, where k > 0 which is read " n choose k-1" + "n choose k" = n+1C k. I tried using the formula for the binomial coefficient, but it becomes very messy. I also tried setting k = 1, but...

Hello all In my calculus book, this problem has been pestering me" Prove nC(k-1) + nCk = (n+1)Ck, where k > 0 which is read " n choose k-1" + "n choose k" = n+1C k. I tried using the formula for the binomial coefficient, but it becomes very messy. I also tried setting k = 1, but...

Hello... 1. In baseball, there are 24 different "base-out" configurations (ruuner out first - two outs, bases loaded - none out and so on). Suppose that a new game, sleazeball, is played where there are seven bases (excluding home plate) and each team gets five outs an inning. How many...

i need help with combinatorics...i need to finda ogf to compute the how many ways can 27 identical walls be distributed into 7 boxes, where the first box can contain at most 9 balls How do this??can you give me a method or explain to me how to do this step by step PLEASE! sAint

I need a little help with combinatorics. 2 Students have 6 dollar notes worth 500 dollars, and 4 notes worth 1000 dollars. Notes with the same value are not distinguished. A-How many ways to split the notes B-How many ways to split the notes, so that both get an equal amount of notes...