A bin contains three components from supplier a, four from supplier b, and five from supplier

c. if four of the components are randomly selected for testing, what is the probability that each supplier would have at least one component tested?

The number of ways to select one component from each supplier is 3*4*5 since you can choose one of three from A, in each case you can then choose 1 of 4 from B and lastly for each selection from A and B you have 5 possible choices for C. After that you have 12-3=9 components left for choice of the fourth component to test. Thus there will be 3*4*5*9 different ways to choose at least one from each supplier.