Final answer:
There are 70,000 6-digit numbers that are even or divisible by 5.
Step-by-step explanation:
To determine the number of 6-digit numbers that are even or divisible by 5, we need to consider two cases: numbers that are even and numbers that are divisible by 5.
Case 1: Even numbers - The last digit must be even, which means it can be any of the digits 0, 2, 4, 6, or 8. The remaining 5 digits can be any of the digits 0-9, excluding the last digit chosen. Therefore, there are 5 choices for the last digit and 10 choices for each of the remaining 5 digits. This gives us a total of 5 * 10 * 10 * 10 * 10 * 10 = 50,000 even 6-digit numbers.
Case 2: Numbers divisible by 5 - The last digit must be 0 or 5. Similar to case 1, the remaining 5 digits can be any of the digits 0-9, excluding the last digit chosen. Therefore, there are 2 choices for the last digit and 10 choices for each of the remaining 5 digits. This gives us a total of 2 * 10 * 10 * 10 * 10 * 10 = 20,000 6-digit numbers divisible by 5.
Adding the results from both cases, we get a total of 50,000 + 20,000 = 70,000 6-digit numbers that are even or divisible by 5.