A lock on a bank vault consists of three dials, each with 30 positions. In order for the vault to open, each of the three dials must be in the correct position. a. How many different possible dial combinations are there for this lock? b. What is the probability that if you randomly select a posi- tion on each dial, you will be able to open the bank vault? c. Explain why "dial combinations" are not mathematical combinations expressed by Equation (4.14).