Letters and envelopes derangement probability

Evaluate the probability/combinatorial statements independently:

Statement 1: If 3 letters match their correct envelopes perfectly, the 4th letter has only one envelope remaining—which must be its correct one. It is logically impossible for exactly one letter to be misplaced. Thus, Statement 1 is false.

Statement 2: We need exactly 2 letters in correct envelopes, meaning the remaining 2 letters must be completely deranged (misplaced). Step 1: Choose which 2 letters are correct: 4{2} = 4 × 3/2 = 6 ways. Step 2: Derange the remaining 2 letters. The number of ways to derange 2 items is exactly 1 (each goes into the other's envelope). Total ways = 6 × 1 = 6 ways. Statement 2 is correct.

Answer: (b).