Exactly 1 nonconforming unit = 0.369458128 1 or more nonconforming units = 0.433497537 Due to formatting issues, I'll use the notion C(n,x) for N choose X. Which would be n!/(x!(n-x)!). Now for the case of exactly 1, the probability will be: P = C(3,1)*C(30-3,4)/C(30,5) To explain it, you choose exactly 1 nonconforming item out of the 3 possible, then fill the sample with 4 more conforming items to complete the sample size of 5. Finally, you divide by the number of different ways you can select 5 items out of the entire group of 30. So doing the math, you get P = C(3,1)*C(30-3,4)/C(30,5) = 3*17550/142506 = 0.369458128 = 36.9458128% For the case of 1 or more nonconforming units you do the sum of x ranging from 1 to 3 with the formula C(3,x)*C(30-3,5-x)/C(30,5) or you can set x to 0 and evaluate 1 - C(3,0)*C(30-3,5-0)/C(30,5) Let's do it both ways. C(3,1)*C(30-3,5-1)/C(30,5) + C(3,2)*C(30-3,5-2)/C(30,5) + C(3,3)*C(30-3,5-3)/C(30,5) = 3*17550/142506 + 3*2925/142506 + 1*351/142506 = 0.369458128 + 0.061576355 + 0.002463054 = 0.433497537
And doing it the "simple" way 1 - C(3,0)*C(30-3,5-0)/C(30,5) = 1 - 1*80730/142506 = 1 - 0.566502463 = 0.433497537