A bin of 50 parts contains 5 that are defective. a sample of 10 parts is selected at random, without replacement. how many samples contain at least four defective parts.

FROM the 5 defective parts , select 4, and the number of ways to complete this step (5!/4!1!) =5 . from the 45 non-defective parts ,select 6, and the number of ways to complete this step 45!/(6!39!) =8,145,060. THEREFORE the number of samples that contain exactly 4 defective parts is 5(8,145,060 )= 40,725,300 , the number of ways to select 5 is 5!(5!1!)=1. from the 45 non-defective parts select 5 and the numbers of ways to complete this step is 45!/(5!40!)=1221759 . therefore the number of samples that contain exactly 5 defective parts is 1(1221759)=41947059. therefore ,the number of samples that contain exactly 5 defective parts is 1(1221759) =1221759 . therefore the number of samples that contain at least four defective parts is 40725300+1221759=41947059