Question

There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5, 6.

The three digit number 536 is one way the dials can be set as shown in the diagram.
a) Work out the number of different three digit numbers that can be set for the combination lock.
b) How many of the possible three digit numbers have three different digits?​

Answer 1

The number of different three-digit numbers that can be set for the combination lock is 216. The number of possible three-digit numbers with three different digits is 120.

Step-by-step explanation:

a) To calculate the number of different three-digit numbers that can be set for the combination lock, we need to find the number of possibilities for each dial and multiply them together. Since each dial can be set to any number from 1 to 6, there are 6 possibilities for each dial. So, the total number of different three-digit numbers is 6 x 6 x 6 = 216.

b) To find the number of possible three-digit numbers with three different digits, we need to consider the choices for each digit. For the first digit, we have 6 options. For the second digit, we have 5 options (since it cannot be the same as the first digit). And for the third digit, we have 4 options. So, the total number of possible three-digit numbers with three different digits is 6 x 5 x 4 = 120.