Probability Maths Question

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I am trying to work this out... and my maths is failing me, I know its basically lottery maths

You have 14000 boxes with balls in them, 350 of the balls are green and the rest are yellow. You want to find as many green balls as possible but you only have 35 chances.

I think the probability of getting one green ball is 8.75%...

But I can't then work out how to calculate the probability of getting 2 green balls or how it steps down to possibly getting all 35. Any one care to assist and save my sanity? :D
 
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Ok let me try the story again lol

There are 14000 boxes in front of you, each box has one ball in.
350 of the balls are green and the rest are yellow.
You want to find as many green balls as possible but you only have time to look in 35 boxes.
Once a ball is found you put it to one side to look for more.

This is a for a non ball related issue where I work but the theory would apply, I can come up with amazing stuff in excel (in my opinion) normally but for some reason my brain isn't just getting this :)
 
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