Use the fundamental counting principle to answer the following question. Using the digits 1,2,3,5,6,8,0 with no repetition allowed, how many four-digit numbers can be constructed if the number is even?

To solve this problem, we can break it down into two steps:

Step 1: Determine the number of choices for each digit in the four-digit number.
- Since the number must be even, the last digit must be either 0, 2, 6, or 8. This gives us 4 choices for the last digit.
- The first digit cannot be 0, so we have 6 choices for the first digit.
- The remaining two digits can be any of the remaining 5 digits (1, 2, 3, 5, 6) since repetition is not allowed. This gives us 5 choices for each of the second and third digits.

Step 2: Apply the fundamental counting principle to find the total number of possibilities.
According to the fundamental counting principle, the total number of possibilities is equal to the product of the number of choices for each digit. Therefore, the total number of four-digit numbers that can be constructed is:
4 \times 6 \times 5 \times 5 = 600

Answer: There are 600 four-digit numbers that can be constructed using the digits 1, 2, 3, 5, 6, 8, and 0 with no repetition allowed if the number is even.