A lock on a bank vault consists of 3 dials, each with 30 positions. In order for the vault to open, each of the three dials must be in the correct position. How many different dial combinations are there for this lock?
Use the multiplication rule if the dial settings are independent of each other.
For example, if we have 4 independent dials each with 5 numbers, then we have 5 choices for each, and multiplication rule gives 5*5*5*5=625 combinations.
30*30*30=
27000
To calculate the total number of different dial combinations for the lock, we need to multiply the number of positions on each dial together.
Given that each dial has 30 positions, multiplying the number of positions on each dial will give us the total number of combinations.
Therefore, the number of combinations for this lock is:
30 x 30 x 30 = 27,000
So, there are 27,000 different dial combinations for this lock.