# Probability of picking all red balls

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.

• What are the methods and their answers? – GoodDeeds Oct 8 '16 at 13:30
• 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. – Graham Kemp Oct 8 '16 at 13:42

For the first draw, there is $5$ out of $50$, for the next there is $4$ out of $49$, etc., so the probability is
$$\frac{5\cdot 4 \cdot 3 \cdot 2 \cdot 1}{50 \cdot 49 \cdot 48 \cdot 47 \cdot 46}=\frac{5!45!}{50!}\approx 4.7197\times 10^{-{7}}.$$