There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:

1. It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.

Which of the statements given above is/are correct?

Statement 1: If one letter is placed in an incorrect envelope, then the letter that belongs to that envelope must also be placed in an incorrect envelope. Therefore, it’s not possible for only one letter to be misplaced; either no letter will be misplaced, or at least two letters will be misplaced. Thus, Statement 1 is incorrect.

Statement 2: To fulfill the requirement of placing two letters in correct envelopes and two in incorrect envelopes, we can choose the two letters to be placed in correct envelopes in 4C2 ways, which equals 6 ways. The remaining two letters will automatically be placed in each other’s envelopes (i.e., incorrect envelopes). Therefore, Statement 2 is correct. Hence, option (b) is the correct answer.