Question

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?

Answer 1

The number of different dial combinations for the lock is 24,360.

Step-by-step explanation:

The number of combinations for the lock can be found using the concept of permutations. Since each dial has 30 positions and there are 3 dials, the number of combinations is calculated by finding the product of the number of positions on each dial. We can use the formula for permutations to find the number of combinations: nP(r) = n! / (n-r)!. In this case, n = 30 (number of positions on each dial) and r = 3 (number of dials). Plugging in these values, we get: 30P3 = 30! / (30-3)! = 30! / 27! = 30 x 29 x 28 = 24,360.

Answer 2

30 x 30 x 30 = 27000