Results 1 to 3 of 3

Math Help - Combinatorics

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Combinatorics

    I'm trying to prepare for a course in discreet mathematics I'll have the next semester so I got a bunch of questions from a friend to help me. So far I've gone trough logic and sets. With this problems presented my biggest problem is that I dont quite understand the questions or how to go about them.

    My first problem is with proofs, as I dont really understand what counts as a proof.

    Well, on to the problems. In one problem I got a 16 letter long word and want to find out how many strings of length 16 I can create out of this word. Some letters apear multiple times in the word. The word I have is schoolmistresses.

    In another problem I got the equation x+y+5z+w=15 and I got to find out how many solution this equation got. I'm not sure how to do this in itself and especially not with the conditions : x; y; z and w are non-negative integers and we also have that x is positive?

    What I dont understand in the condition is that first we say that the variables must be non negative integers , for example 1,2,3,4,5... and then we have that x must be positive. Isn't that redundant or is there something I'm missing.

    The third problem is where I must prove something.

    We assume the following statement is true: there are inifnitely many positive integers Mk
    such that all the binomial coefficients C(Mk; j); 1 <= j <=Mk - 1 are even integers

    Prove that there are also inifnitely many positive integers nk such that all the binomial coefficients C(Nk; j); 0<=j <= Nk are odd integers.

    In this part I understand that I should first start with understanding what a binominal coeffient is. Also if I understood the first sentence correct, the expression C(Mk,j) is always true for 1<=j<=Mk-1. Do I read this correct.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Combinatorics

    Quote Originally Posted by dipsy34 View Post
    Well, on to the problems. In one problem I got a 16 letter long word and want to find out how many strings of length 16 I can create out of this word. Some letters apear multiple times in the word. The word I have is schoolmistresses.

    In another problem I got the equation x+y+5z+w=15 and I got to find out how many solution this equation got. I'm not sure how to do this in itself and especially not with the conditions : x; y; z and w are non-negative integers and we also have that x is positive?
    I will help with these two.
    The first follows the standard example: consider MISSISSIPPI. There are there are eleven letters there: four S's, four I's, and two P's are repeated.
    There are \frac{11!}{(4!)(4!)(2!)} ways to rearrange that word.
    We divide to eliminate the over counts.


    For x+y+5z+w=15 the 5 complicates things.
    The z can only four values: 0,1,2,3

    You should know that x+y+w=15 has \binom{15+3-1}{15} non-negative integral solutions. So that takes care of z=0.

    Now for z=1, \binom{10+3-1}{10}. Why the 10? Because we have already used 1(5)=5 of the ones.

    To finish do that for z=2,3 and add the four results.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Re: Combinatorics

    Quote Originally Posted by Plato View Post
    There is just one thing I dont understand with the last part and that is how you come up with 15+3-1?
    Thanks for the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Combinatorics.
    Posted in the Discrete Math Forum
    Replies: 16
    Last Post: July 20th 2010, 02:29 AM
  2. Combinatorics
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: June 18th 2010, 08:14 PM
  3. Combinatorics
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: June 3rd 2010, 05:24 PM
  4. combinatorics
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 1st 2010, 10:53 PM
  5. Combinatorics
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 10th 2009, 06:03 AM

Search Tags


/mathhelpforum @mathhelpforum