Question

How many four-digit personal identification numbers (PIN) are possible if the PIN cannot begin or end with a 0, and the PIN must be an even number?

Option 1: 3,600
Option 2: 4,000
Option 3: 4,500
Option 4: 8,100

Answer 1

There are 4,500 possible four-digit PINs that meet the given criteria.

Step-by-step explanation:

To determine the number of possible four-digit PINs that meet the given criteria, we can break down the problem into three steps:

1. Exclude the possibility of starting or ending with 0 which leaves us with 9 options.
2. Consider that the PIN has to be an even number, so the last digit has to be 0, 2, 4, 6, or 8. This gives us 5 options for the last digit.
3. For the remaining two digits in the PIN, there are 10 options for each digit since repetition is allowed.

Therefore, the total number of possible four-digit PINs is 9 (options for the first digit) × 5 (options for the last digit) × 10 (options for the second digit) × 10 (options for the third digit) = 4,500.