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I am really struggling to solve this problem, I hope someone can help and show me how its worked out as my two methods give different answers.

What is the probability that I would pick out all $5$ red balls from a bucket that contained $5$ red balls and $45$ black choosing one ball at a time without replacing the balls taken.

The fractoral method gives me a different answer than the other. I think it's because they are picked out one at a time rather than all at once Thanks.

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    $\begingroup$ What are the methods and their answers? $\endgroup$
    – GoodDeeds
    Commented Oct 8, 2016 at 13:30
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    $\begingroup$ Picking out one at a time, or all at once, makes no difference to probability calculations when the event description does not involve order of selection. $\endgroup$
    – Graham Kemp
    Commented Oct 8, 2016 at 13:42

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For the first draw, there is $5$ out of $50$, for the next there is $4$ out of $49$, etc., so the probability is

$$\frac{5\cdot 4 \cdot 3 \cdot 2 \cdot 1}{50 \cdot 49 \cdot 48 \cdot 47 \cdot 46}=\frac{5!45!}{50!}\approx 4.7197\times 10^{-{7}}.$$

This is assuming that you only draw five balls in total. If this is not the case, please let me know (you then have to use binomial coefficients).

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  • $\begingroup$ Did you mean 5 out of 50 for the first step? $\endgroup$
    – Alex
    Commented Oct 10, 2016 at 8:19
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    $\begingroup$ @Alex Yes, thank you - corrected now! $\endgroup$
    – Bobson Dugnutt
    Commented Oct 10, 2016 at 17:28

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