What is the difference between the greatest 4-digit number and the least 4-digit number formed by using the digits 1, 5, 0 and 7 once?

The correct option is 6453.

To find the difference between the greatest and the least 4-digit numbers formed by using the digits 1, 5, 0, and 7 exactly once, we follow these steps:

Step 1: Form the greatest 4-digit number
To form the greatest number, we arrange the given digits in descending order (from largest to smallest):
7 > 5 > 1 > 0
Thus, the greatest 4-digit number is 7510.

Step 2: Form the least 4-digit number
To form the least 4-digit number, we arrange the digits in ascending order (from smallest to largest): 0, 1, 5, 7.
However, a number cannot begin with the digit 0 as it would then become a 3-digit number (0157 is equal to 157).
Therefore, we place the smallest non-zero digit (which is 1) at the thousands place, and then place 0 followed by the remaining digits in ascending order.
Thus, the least 4-digit number is 1057.

Step 3: Calculate the difference
Now, we subtract the least 4-digit number from the greatest 4-digit number:

$7510-1057=6453$

Therefore, the difference between the greatest and the least 4-digit numbers formed by the given digits is 6453.