Question

Vijay wrote 4 different letters to send to 4 different addresses. For each letter, he prepared one envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, in how many ways can we put the letters so that only two of the letters goes to the right envelopes?

• A. 2
• B. 4
• C. 1
• D. 6

Answer 1

The correct option is D

6

We have to select two letters to put in the correct envelopes. We can select two of the four letters in ${}^4{C}_2=6$ ways the leftover 2 letters must be put in the wrong envelopes. There is only 1 way of ensuring that the other two letters go into the wrong envelopes. Hence, total number of ways such that only two letters go into the correct envelopes = 6*1 = 6 ways