Final answer:
To find the greatest and smallest numbers, arrange the digits in ascending and descending order.
Step-by-step explanation:
The question is asking to determine the greatest and smallest number that can be formed using the digits 4, 0, 7, 2, 8. To get the greatest number, we arrange the digits in descending order, while to get the smallest number, we arrange the digits in ascending order, keeping in mind that the smallest number cannot start with the digit 0 as it wouldn't be considered a valid five-digit number.
The greatest number is therefore 87420 - obtained by arranging the digits as 8, 7, 4, 2, 0. The smallest number is 20478 - obtained by arranging the digits as 2, 0, 4, 7, 8, ensuring that the 0 is not at the beginning.
So the answer is B: 87420, 20478.