Question

how many ways can a 4 digit passcode be selected if the numbers must be distinct and it must be even and the numbers must be between 0-7

Answer 1

Since it must be even, start with the last digit. It can be 0, 2, 4, or 6, (4 options).

Now look at any other digit, it can be any number between 0-7 EXCEPT the number chosen for the last digit (say you choose 0, then it could be 1-7). That means there could be 7 options.

The third digit is similar to the second, but there are 2 numbers already taken. Therefore there are 6 options.

Finally, the final digit is like the second and third. Since there are 3 numbers taken, there are 5 options.

4 * 7 * 6 * 5 = 840 different ways