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  4. There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is

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Q. There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is

Permutations and Combinations

Solution:

There is concept of derangement. The required number is
$4![1 - \frac{1}{1!} + \frac{1}{2!} -\frac{1}{3!} + \frac{1}{4!}] = 9$