What is the difference between the largest and the smallest 7-digit number that can be formed using the digits 9, 0, 5, 2, 7, 1, 4 exactly once?
Options
8,729,631
8,808,740
8,700,000
8,800,000
Explanation
The given digits are 9, 0, 5, 2, 7, 1, 4.\nTo form the largest 7-digit number, arrange the digits in descending order: 9, 7, 5, 4, 2, 1, 0. So, the largest number is 9,754,210.\nTo form the smallest 7-digit number, arrange the digits in ascending order. However, 0 cannot be the first digit. So, we place the smallest non-zero digit first, which is 1, followed by 0, and then the remaining digits in ascending order: 1, 0, 2, 4, 5, 7, 9. So, the smallest number is 1,024,579.\nNow, calculate the difference between the largest and smallest numbers:\nDifference = 9,754,210 - 1,024,579 = 8,729,631.