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Math Help - stuck

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    13

    stuck

    I dont have a clue, I need to get these examples out , they are hints for exam, please help!
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  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
    13

    sorry, forgot to post q's

    (1) Let
    k be any positive integer. Prove that there exists a positive
    integer multiple
    n of k such that the only digits in n are 0s and
    1s. (Use the pigeonhole principle.)
    (2) A
    ternary string is a sequence of 0s, 1s and 2s. How many
    ternary strings of length 12 are there? How many of those
    strings contain exactly five 0s, three 1s and four 2s? How many
    ternary strings of length 12 contain an odd number of 1s?
    (3) Prove the binomial identity

    X
    n
    i
    =0

    
    n
    i
    
    2

    =
    
    2
    n
    n

    
    .
    (4) A committee of seven people is to be chosen from twelve married
    couples. How many ways can a committee of three men and four
    women be chosen? How many ways can a committee containing
    no married couple be chosen? How many ways can a committee
    containing exactly two married couples be chosen?
    (5) Find the number of non-negative integer solutions of
    x
    1 + x2 + x3 + x4 + x5 = 7.

    How many of those solutions have xi  0 for all i?
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