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Math Help - Question about Probability - Arrange set of Numbers

  1. #1
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    Question about Probability - Arrange set of Numbers

    Dear all, I was given a set of number "0000011" and asked how many different arrangement I can make with only this set of number.

    I tried to list all possible arrangements (0100001, 0001001.......) But it takes way too long. I am think of using the formula of Permutation, am i on the right track?

    Thanks!
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  2. #2
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    Hello, mak15!

    I was given a set of number "0000011"
    and asked how many different arrangements I can make with this set of number.
    Due to the simplicity of the given number, it is a Combination problem.


    We will have a 7-digit number: ._ _ _ _ _ _ _

    Select 2 of the position in which to place the 1's.
    (The 0's will go in the remaining positions.)

    The answer is: . _7C_2 \:=\:{7\choose2} \:=\:\frac{7!}{2!\,5!} \:=\:21 arrangements.

    Last edited by Soroban; November 21st 2009 at 04:09 AM.
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  3. #3
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    Thank you so much! But still confused.

    If I change "0000011" to "abcdeff", will I use the same formula?
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  4. #4
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    Quote Originally Posted by mak15 View Post
    If I change "0000011" to "abcdeff", will I use the same formula?
    No you do not.
    In that case you have seven with two repeats. So \frac{7!}{2!}.

    If you had "10aabbbccccddddd" \frac{16!}{(2!)(3!)(4!)(5!)}
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