# combinatorics

1. ### Combinatorics Problem. I'm stuck plz help

Hi all, I'm new to the forum and looking for some help. So I'm in a combinatorics class, and a lot of the material is over my head, so I'm looking to see if any of you guys would be able to help. I'll list the problem, and also post what I have figured out so far. 2A) Population growth with...
2. ### Probability problem. Possibly involves combinatorics.

Hi, I'm a mature student undertaking a self-study A-Level course in order to go to university. I have been unable to figure this out by myself and have even had a private tutor stumped by it, so any help would be greatly appreciated. It's from "Understanding Statistics" by Upton & Cook...
3. ### Prove by interpreting the parts in terms of compositions of integers. Combinatorics.

Given the identity \sum_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k} Need to give a combinatorial proof by interpreting the parts in terms of compositions of integers (neither by induction nor using subsets) :) Please, help!
4. ### How many words can be made from REGULATION where the vowels are in alphabetical order

Hi Gus, I have the following math problem that I am stuck on: How many words can be made from REGULATION where all the vowels are in alphabetical order? I solved it two different ways and got two different answers. 1. I did 10C5 for choosing 5 spots then multiplied by 1 for the one order the...
5. ### Combinatorics Multiplication Principles

Hi in my book the multiplication principle is stated as follows. Suppose a procedure can be broken into m successive ordered stages,with r1 different outcomes in the first stage r2 different out comes in the second stage... And rm different outcomes in the mth stage. if the number of...
6. ### How do I use Combinatorics to read Venn diagrams?

The problem looks like this: Stephen asked 100 coffee drinkers whether they like cream or sugar in their coffee. According to the Venn diagram below, how many like: a) Cream? b) Sugar? c) Sugar but not cream? d) Cream but not sugar? e) Cream and sugar? f) Cream or sugar? g) Black (no...
7. ### Combinatorics

Hi, I need a little bit help with this: Got to work my way from "sum from k=1 to n (k^2*n nCr k))" to this: (n^2+n)*2^(n-2), but HOW? I´ve tried god-knows-what but nothing seems to work..
8. ### Combinatorics question

So you have 12 players paul can play all 3 positions, 5 can only play center or forward and 6 can only play guard. How many basketball lineups can be made? (there are 1 center 2 guards and 2 forwards and the order of guards and forwards doesn't matter) we have c1,f1,f2,g1,g2 are the positions...
9. ### Sum of first m terms of a combinatorial number

Dear Math Help Forum, 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 with...
10. ### Distribution of three kinds of objects

Hi. This problem sounds seemingly simple but I am not sure if it's as simple as I think so I've decided to post it here. We have three kinds of objects and there are 2n objects of each kind. How many ways of dividing those 6n objects between two people are there so that each of them gets 3n...
11. ### Average number, combinatorics

Please help me solve these problems. 1. Nine boys and fourteen girls are arranged in a row in all possible ways. What is the average number of "neighbours" of opposite sex. 2. Consider a family of all k-element subsets of a set \left\{ 1,2,......,2n\right\}. For every such set consider its...
12. ### sequences of natural numbers whose sum is n

Please help me solve these two problems. To be honest, I would really appreciate something more than just a small hint, because I have really no idea how to go about solving it ;( 1. Consider all possible sequences of natural numbers whose sum is n . Each sequence has a certain number of...
13. ### Secret Sharing

Six scientists are working on a secret project. They wish to lock up the documents in a cabinet so that the cabinet can be opened when and only when three or more of the scientists are present. What is the smallest number of locks needed? What is the smallest number of keys each scientist must...
14. ### A cloak covered with patches

Hi. Could you help me solve this problem. I've tried using inclusion–exclusion principle but it didn't work. There is a cloak which area equals 1. It is completely covered with 5 patches, whose area is at least 0,5. Show that the area of the intersection of certain two patces is at least 0,2...
15. ### Combinatorics homework help?

I know these should be relatively simple but combinatorics has always been my Achilles heel. If you could explain these to me that would be awesome? I am really struggling to wrap my head around how you do these. How many 5 card hands have two or more kings? How many 5 card hands contain the...
16. ### Combinatorics QUESTION

Let A = {a_1, a_2, . . . , a_k} be an alphabet, and let n_i denote the number of appearances of letter a_i in a word. How many words of length n in the alphabet A are there for which k = 3, n = 10, n_1 = n_2 + n_3 and n_2 is even?
17. ### Combinatorics QUESTION 3-3

Let n be an odd integer greater than 1. Prove that the sequence (n choose 1), (n choose 2) , . . . , {n choose (n−1)/2} contains an odd number of odd numbers.
18. ### Combinatorics QUESTION 2-3

Let A = {a_1, a_2, . . . , a_k} be an alphabet, and let n_i denote the number of appearances of letter a_i in a word. How many words of length n in the alphabet A are there for which k = 3, n = 10, n_1 = n_2 + n_3 and n_2 is even?
19. ### Combinatorics QUESTION 1-3

Nine chairs in a row are to be occupied by six students and three professors. The three professors arrive before the six students and decide to choose their chairs so that each professor will be between two students. In how many ways can the professors choose their chairs?
20. ### Combinatorics - Tim Tams!

I have been attempting to figure out the below question for over two hours. Could someone please help me towards a solution. Combination formula is not working for me. "In how many ways can a packet of 24 TimTams be distributed amongst 6 chocoholics, so that nobody gets more than 8 Tim Tams."