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?

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Solution

The correct options are
C
1

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

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