There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the

Question

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?

Accepted Answer

Here is the explanation for why option B is correct:

Analysis of Statement 1:
If there are four letters and four envelopes, and three letters are placed in their correct envelopes, the fourth letter must also automatically go into its correct envelope. It is mathematically impossible for exactly one letter to be in the wrong envelope because the error would have no other letter to swap places with. Therefore, statement 1 is incorrect.

Analysis of Statement 2:
To have exactly two letters in the correct envelopes, we must first choose which 2 letters out of 4 are correct. The number of ways to choose 2 letters is calculated as 4 choose 2, which equals 6 ways. For each of these 6 cases, the remaining 2 letters must both be in the wrong envelopes. There is only 1 way for two remaining letters to both be wrong they must be swapped. Thus, 6 multiplied by 1 equals 6 total ways. Therefore, statement 2 is correct.

Conclusion:
Since statement 1 is false and statement 2 is true, the correct option is B.

Answer

1 only

Answer

2 only

Answer

Both 1 and 2

Answer

Neither 1 nor 2

Explanation

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