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Math Help - Finding amount of numbers.

  1. #1
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    Smile Finding amount of numbers.

    I need help with finding how many 8-digit numbers there are containing no more than three zeros?
    For exampel numbers like 10001111.

    Thanx in advance.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Monika1987 View Post
    I need help with finding how many 8-digit numbers there are containing no more than three zeros?
    For exampel numbers like 10001111.

    Thanx in advance.
    Can you think of a way of finding out how many numbers have no zeros? one zero? Two zeros? Three zeros?

    (Hint: you have 8 places, and you are choosing none to be a zero, then one to be a zero, then two to be a zero, then three to be a zero...)

    Finally, subtract these from the total number of numbers to get your result!
    Last edited by Swlabr; March 10th 2010 at 01:03 AM.
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  3. #3
    MHF Contributor chisigma's Avatar
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    A quick alternative is the use of 'binomial coefficients'. The number of way to dispose k zeroes in a numer of n digits is ...

    \binom{n}{k} = \frac{n!}{k!\cdot (n-k)!} (1)

    ... so that the number of 8 digits numbers having no more than 3 zeroes is...

    N= \binom{8}{0} + \binom{8}{1} + \binom{8}{2}+ \binom{8}{3} (2)

    Kind regards

    \chi \sigma
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