No Correct Letter

This is the derangement problem for $n=4$.

Use $D_n=n!{\sum }_{k=0}^n\frac{(-1{)}^k}{k!}$.

1. 1. Count derangements

   The number of derangements of 4 objects is $D_4=9$.

2. 2. Total permutations

   There are $4!=24$ total permutations.

3. 3. Probability

   Probability is $9/24=3/8$.

   $$P=\frac{9}{24}=\frac{3}{8}$$

Answer: 3/8