The position of how many digits will remain the same , if the digits in the number 97215368 are rearranged in the descending order ?

Options

A. None
B. One
C. Two
D. Three

Explanation

To solve the problem, we need to rearrange the digits of the number 97215368 in descending order and then check how many digits remain in the same position as they were in the original number.

### Step-by-step Solution:

1. **Write down the original number**:
The original number is 97215368.

2. **List the digits**:
The digits in the number are: 9, 7, 2, 1, 5, 3, 6, 8.

3. **Rearrange the digits in descending order**:
To arrange the digits in descending order, we start with the largest digit and go to the smallest:
- The largest digit is 9.
- The next largest is 8.
- Then we have 7.
- Next is 6.
- Then 5.
- After that, we have 3.
- Next is 2.
- Finally, the smallest digit is 1.

Thus, the digits arranged in descending order are: 9, 8, 7, 6, 5, 3, 2, 1.

4. **Compare the original and rearranged digits**:
Now we compare the original number with the rearranged number to see which digits remain in the same position:
- Original: 9, 7, 2, 1, 5, 3, 6, 8
- Rearranged: 9, 8, 7, 6, 5, 3, 2, 1

Let's check each position:
- Position 1: 9 (same)
- Position 2: 7 (changed)
- Position 3: 2 (changed)
- Position 4: 1 (changed)
- Position 5: 5 (changed)
- Position 6: 3 (same)
- Position 7: 6 (changed)
- Position 8: 8 (changed)

5. **Count the positions that remain the same**:
From our comparison, the digits that remain in the same position are:
- Position 1: 9
- Position 6: 3

Therefore, there are **2 digits** that remain in the same position.

### Final Answer:
The number of digits that remain in the same position is **2**.

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