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Math Help - probability with combination

  1. #1
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    probability with combination

    There are k sets of numbers : {0,1,2,.,m1}, {0,1,2,..,m2}, ,{0,1,2,,mk}
    Such that m1<m2<<mk.
    1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?
    2. What is the probability that any two sets will have at least one element common ?
    (Please provide procedure and explanation)

    I think the answer given by Plato is the number of permutations, but I am looking for the number of combinations i.e., the sets with all elements same (although in different order) will be treated as one.

    AND Plz mention the rule/formula name with explanation so that I can learn them
    Last edited by achal; December 17th 2011 at 01:06 AM.
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  2. #2
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    Re: probability with combination

    Quote Originally Posted by achal View Post
    There are k sets of numbers : {0,1,2,.,m1}, {0,1,2,..,m2}, ,{0,1,2,,mk}
    Such that m1<m2<<mk.
    1. How many combinations of k elements can be made taken 1 element from each set such that each set has all distinct elements (no two elements are equal) ?
    I for one find this question hard to follow.
    Here is the way I read it.
    There is a increasing sequence of integers: 0<m_1<m_2<\cdots<m_k.
    There are sets A_n=\{1,2,\cdots,m_n\}.
    We pick a number from A_1, then we pick a different number from A_2, etc until we pick yet a different number from A_k. Thus we have k different selections.

    The question seems to be, "How many different selections are possible?"

    Note the the number of integers in each set is \|A_n\|=m_n+1.
    If this is the correct setup, the answer is:
    \prod\limits_{n = 1}^k {\left( {m_n  + 2 - n} \right)}
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