The difference between the greatest and the least five-digit numbers formed by the digits 2, 5, 0, 6 and 8 is (repetition of digits is not allowed)

Options

A. 69552
B. 65925
C. 65952
D. 63952

Answer

To solve the problem of finding the difference between the greatest and least five-digit numbers formed by the digits 2, 5, 0, 6, and 8 (without repetition of digits), we can follow these steps:

### Step 1: Identify the greatest five-digit number
To find the greatest five-digit number, we should arrange the digits in descending order. The digits we have are 2, 5, 0, 6, and 8.

- Arranging these digits from highest to lowest gives us: 8, 6, 5, 2, 0.
- Therefore, the greatest five-digit number is **86520**.

### Step 2: Identify the least five-digit number
To find the least five-digit number, we need to arrange the digits in ascending order, but we cannot start with 0 (as it would not be a five-digit number).

- The smallest non-zero digit we have is 2. So we start with 2.
- Next, we can use 0, followed by the remaining digits in ascending order: 5, 6, and 8.
- Thus, the least five-digit number is **20568**.

### Step 3: Calculate the difference
Now, we need to find the difference between the greatest and least five-digit numbers we calculated.

- Greatest number: 86520
- Least number: 20568

Now, we perform the subtraction:

\[ 86520 - 20568 \]

### Step 4: Perform the subtraction
Let's do the subtraction step by step:

1. Subtract the units place: \(0 - 8\) (we need to borrow, so it becomes \(10 - 8 = 2\)).
2. Subtract the tens place: \(1 - 6\) (again, we borrow, so it becomes \(11 - 6 = 5\)).
3. Subtract the hundreds place: \(4 - 5\) (we borrow, so it becomes \(14 - 5 = 9\)).
4. Subtract the thousands place: \(5 - 0 = 5\).
5. Subtract the ten-thousands place: \(8 - 2 = 6\).

Putting it all together, we get:

\[ 86520 - 20568 = 65952 \]

### Final Answer
The difference between the greatest and least five-digit numbers formed by the digits 2, 5, 0, 6, and 8 is **65952**.

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