Question

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

Answer 1

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.