Five students are made to stand in a single row according to the following rules: 1.

Based on the constraints, the only possible arrangement of students from left to right is E, D, C, B, A. In this sequence, B is positioned exactly between C and A, making Conclusion 1 true and Conclusion 2 false.

Step-by-step Derivation:
Step 1: Identify the total number of positions: 5 (1st, 2nd, 3rd, 4th, 5th from left to right).
Step 2: Apply Rule 3: E is at the extreme left end. Position 1 = E.
Step 3: Apply Rule 4: B is second from the right. Position 4 = B.
Step 4: Apply Rule 1: A and B are next to each other. A must be at Position 3 or Position 5. However, Rule 3 states A is not next to E (Position 1), which doesn't restrict A from 3 or 5. Let's check other rules first.
Step 5: Apply Rule 6: B and C are standing together. C must be at Position 3 or Position 5. Since B is at Position 4, C can be at 3 or 5.
Step 6: Apply Rule 2: C and D are next to each other. If C is at Position 5, D must be at Position 4, but B is already at Position 4. Therefore, C must be at Position 3. Position 3 = C.
Step 7: Since C is at Position 3, D must be at Position 2 (because Position 4 is B). Position 2 = D.
Step 8: Now determine A's position. A must be next to B (Rule 1). The only remaining spot is Position 5. Position 5 = A.
Step 9: Verify Rule 5: C (Pos 3) is to the right of D (Pos 2) and E (Pos 1). This is correct.
Step 10: Final Sequence: E (1), D (2), C (3), B (4), A (5).
Step 11: Evaluate Conclusions:

• Conclusion 1: B is between C (3) and A (5). This is TRUE.
• Conclusion 2: A is between C and B. This is FALSE (A is at the end).