Hi All, I am trying to reconcile two approaches used in counting problems. The first approach uses combinations and the other uses probability. I understand the combinations approach, but not able to comprehend the probability approach. Consider the following example, A carton contains 12 toasters, 3 of which are defective (D). If four toasters are sold at random, find the probability that exactly one will be defective. By the combinations approach: 3C1 * 9C3 / 12C4 = 252/495 = 0.509 Now the probability approach : I am purposely want to use here permutations and not combinations. total possible permutations = 12P4 =11880 Another way of finding the total permutations is to find the chance of getting any permutation = 1/12 * 1/11* 1/10*1/9 = 0.000084. The reciprocal of this number gives the number 11880. My confusion starts now. Consider the case DGGG, where G = Good, and D= Defective. P (DGGG) = 3/12 * 9/11 * 8/10 * 7/9 = 0.127 If we divide this number by the probability of each permutation, 0.000084, we get 1512. Thus, DGGG accounts for 1512 permutations or 1512 / 24 = 63 combinations. I am having a hard time understanding how these 1512 permutations or 63 combinations look like. Could you please help me with this? Thanks, MG.