Question 274529
probability that 0 out of 3 are defective is 8/10 * 7/9 * 6/8 * 1 = .466666667


probability that 1 out of 3 are defective is 2/10 * 8/9 * 7/8 * 3 = .466666667


probability that 2 out of 3 are defective is 2/10 * 1/10 * 8/8 * 3 = .066666666


sum of all probabilities equals 1.


probability that 3 out of 3 are defective is 2/10 * 1/10 * 0/8 = 0


the multipliers are as follows:


set of 3 with all defective = ddd = multiplier of 1.


set of 3 with 1 defective = dnn + ndn + nnd = multiplier of 3.


set of 3 with 2 defective = ddn + dnd + ndd = multiplier of 3.


to see how the multipliers work, consider the probability that 1 out of 3 is defective.


p(dnn) = 2/10 * 8/9 * 7/8 = (2*8*7)/(10*9*8) = 112/720 = .155555555


p(ndn) = 8/10 * 2/9 * 7/8 = (8*2*7)/(10*9*8) = 112/720 = .155555555


p(nnd) = 8/10 * 7/9 * 2/8 = (8*7*2)/(10*9*8) = 112/720 = .155555555


The probability of each of these occurrences is the same so you take one of them and multiply it by 3 and you get the same answer.