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Thread: partioning sets...

  1. #1
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    partioning sets...

    a set has 5 members.what is the the number ways of partioning it into 2 or more subsets???
    please help
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  2. #2
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    What things are you given and roughly what knowledge are you supposed to use?
    Last edited by Vlasev; Aug 11th 2010 at 11:41 PM.
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  3. #3
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    all i have is the question.
    you should be able to answer it with only high school maths.
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  4. #4
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    Quote Originally Posted by earthboy View Post
    a set has 5 members.what is the the number ways of partioning it into 2 or more subsets???
    Quote Originally Posted by earthboy View Post
    all i have is the question.
    you should be able to answer it with only high school maths.
    I do not consider this to a high school level question.
    So I am giving you the technical answer. But I cannot explain to you.
    The fifth Bell number is $\displaystyle \mathcal{B}(5)=52$.
    That is the number of ways to partition a set of five.
    But one of those is the set itself, so it does meet the condition of ‘two or more subsets’.
    Thus you answer must be $\displaystyle 51$.
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  5. #5
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    Quote Originally Posted by earthboy View Post
    all i have is the question.
    you should be able to answer it with only high school maths.
    You could try it using $\displaystyle n_C_r=\frac{n!}{r!(n-r)!}$

    You cannot have more than 4 members in a subset.
    A subset must contain at least one member.

    Therefore you could list the possibilities, then count the number of ways those possibilities can occur.

    (a) 4 members in a subset and 1 member in the other subset

    For this option, you can count using combinations the number of ways to select 4 from 5 or 1 from 5.


    (b) (i) 3 members in a subset and 2 members in another subset

    You only need to count the number of ways of selecting 3 from 5 or 2 from 5.
    (Selecting any 3 automatically selects the remaining 2 and vice versa)

    (b) (ii) 3 members in a subset and 2 subsets containing 1 member

    You only need to count the number of ways to choose 3 from 5.


    (c) (i) 2 members in a subset and 2 members in another subset
    ..........(the 5th member automatically makes the 3rd subset of 1)


    Select 4 of the 5 and count the number of ways to form 2 groups of 2.
    Hence, first count the number of ways to select 4 from 5,
    then for each group of 4, count the number of ways to pair one member with one of the other 3.


    (c) (ii) 2 members in a subset and the other 3 making single-member subsets

    Select 2 from 5 as the remainder automatically form the single-member subsets.


    (d) One member per subset
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