Say we have NA blue balls and NB red balls mixed together in an urn. When we pick a ball it leaves the urn. I want to find the probability of picking n red balls in a row. The probability of picking a red ball is: NA/(NA+NB) But each time a red ball leaves the urn the probability of picking the next will be: (NA-1)/(NA+NB-1) So in general for n successive red ball picks the probability must be: p(n) = ∏i=0n(NA-1)/(NA+NB-i) First of all I want to ask if this is correctly deduced. Secondly, I want to know if you can evaluate a product like the above in a closed form.