If all the persons sit in alphabetical order from left to right then the position of how many persons remain unchanged?

Study the following information carefully and answer the questions given below:
Seven persons -M, N, O, P, Q, R and S sit in a linear row and facing the north but not necessarily in the same order.
Only four persons sit between P and Q who does not sit at the extreme end of the row. S sits to the immediate right of Q. The number of persons sitting to the right of S is same as the number of persons sitting between M and N who sits to the immediate left of R. O sits to the left of R.

To find how many persons' positions remain unchanged when they sit in alphabetical order from left to right, we first need to determine the original linear arrangement of the seven persons: M, N, O, P, Q, R, and S.

Let the seven positions in the row be numbered 1 to 7 from left to right:
_ _ _ _ _ _ _ (1 to 7, facing North)

Step 1: Analyze the positions of P and Q
According to the clues:
- "Only four persons sit between P and Q who does not sit at the extreme end of the row."
Since there are 4 persons between P and Q, the distance between their positions is 5 (e.g., positions 1 and 6, or 2 and 7).
Since Q cannot sit at either extreme end (positions 1 and 7), the possible placements are:
- Case 1: P is at position 1 and Q is at position 6.
- Case 2: Q is at position 2 and P is at position 7.

Step 2: Place S relative to Q
- "S sits to the immediate right of Q."
Applying this to our cases:
- In Case 1: S must be at position 7 (immediate right of Q at position 6).
The arrangement looks like: P, _, _, _, _, Q, S
- In Case 2: S must be at position 3 (immediate right of Q at position 2).
The arrangement looks like: _, Q, S, _, _, _, P

Step 3: Analyze the positions of M, N, R, and O
According to the clues:
- "N sits to the immediate left of R." (This means N and R sit together in the order NR).
- "The number of persons sitting to the right of S is same as the number of persons sitting between M and N."
- "O sits to the left of R."

Let us test Case 1 (P is at 1, Q is at 6, S is at 7):
- The number of persons sitting to the right of S (position 7) is 0.
- Therefore, the number of persons sitting between M and N must also be 0. This means M and N sit adjacent to each other.
- Since N is immediately to the left of R, and M is adjacent to N, the only possible consecutive block for M, N, and R is M-N-R (since R is already immediately to the right of N).
- The vacant positions in Case 1 are 2, 3, 4, and 5. We must place the block M-N-R and the remaining person O in these slots.
- If we place M-N-R at positions 2, 3, and 4, then O must be placed at position 5. However, this violates the condition "O sits to the left of R" (since O at 5 would be to the right of R at 4).
- If we place M-N-R at positions 3, 4, and 5, then O must be placed at position 2. This satisfies the condition "O sits to the left of R" (since O at 2 is to the left of R at 5).
Thus, the final arrangement for Case 1 is:
1: P, 2: O, 3: M, 4: N, 5: R, 6: Q, 7: S

Step 4: Verify with alphabetical order
Let's list the original arrangement and compare it to the alphabetical order (M, N, O, P, Q, R, S) from left to right:
- Original Arrangement: P, O, M, N, R, Q, S
- Alphabetical Arrangement: M, N, O, P, Q, R, S

Comparing the positions one-by-one:
- Position 1: P vs M (Changed)
- Position 2: O vs N (Changed)
- Position 3: M vs O (Changed)
- Position 4: N vs P (Changed)
- Position 5: R vs Q (Changed)
- Position 6: Q vs R (Changed)
- Position 7: S vs S (Unchanged)

Only the position of S (one person) remains unchanged.