How many digits in the number $53786589$ will remain in the same position when the digits are arranged in ascending order from right to left?

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**Solution:**

1. The given number is $53786589$. Let's write down the digits with their positions from left to right:
   - Position 1: 5
   - Position 2: 3
   - Position 3: 7
   - Position 4: 8
   - Position 5: 6
   - Position 6: 5
   - Position 7: 8
   - Position 8: 9

2. We need to arrange the digits in ascending order **from right to left**. This means the rightmost digit will be the smallest, and the leftmost digit will be the largest.

3. First, list the digits in ascending order:
   $$3, 5, 5, 6, 7, 8, 8, 9$$

4. Now place them from right to left:
   - Position 8 (rightmost): 3
   - Position 7: 5
   - Position 6: 5
   - Position 5: 6
   - Position 4: 7
   - Position 3: 8
   - Position 2: 8
   - Position 1 (leftmost): 9

5. Compare the original digits with the new arrangement at each position:
   - Position 1: Original 5 vs New 9 → Different
   - Position 2: Original 3 vs New 8 → Different
   - Position 3: Original 7 vs New 8 → Different
   - Position 4: Original 8 vs New 7 → Different
   - Position 5: Original 6 vs New 6 → Same
   - Position 6: Original 5 vs New 5 → Same
   - Position 7: Original 8 vs New 5 → Different
   - Position 8: Original 9 vs New 3 → Different

6. Only the digits at positions 5 and 6 remain unchanged.

**Answer:** Two

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