Hao Yu wrote three letters and three envelopes, and he needs to put each letter into the corresponding envelope, with only one letter in each envelope. The number of all possible scenarios where at least one letter is placed incorrectly is $\qquad$ kinds.
Counting.
(Method One)
Assume letters $A, B, C$ correspond to envelopes $a, b, c$;
(1) Only one letter is placed incorrectly: does not exist;
(2) Only two letters are placed incorrectly: there are 3 ways;
(1) Letter $A$ is placed in envelope $b$, letter $B$ is placed in envelope $a$, letter $C$ is placed in envelope $c$;
(2) Letter $A$ is placed in envelope $c$, letter $C$ is placed in envelope $a$, letter $B$ is placed in envelope $b$;
(3) Letter $B$ is placed in envelope $c$, letter $C$ is placed in envelope $b$, letter $A$ is placed in envelope $a$;
(3) All three letters are placed incorrectly: there are 2 ways;
(1) Letter $A$ is placed in envelope $b$, letter $B$ is placed in envelope $c$, letter $C$ is placed in envelope $a$;
(2) Letter $A$ is placed in envelope $c$, letter $C$ is placed in envelope $b$, letter $B$ is placed in envelope $a$; In summary, the total number of possible scenarios where at least one letter is placed incorrectly is $0+3+2=5$.
(Method Two)
Three letters are placed into three envelopes, with one letter per envelope, there are $P_{3}^{3}=3 \times 2 \times 1=6$ different scenarios;
Among them, there is 1 scenario where all three letters are placed in their corresponding envelopes;
Therefore, the total number of possible scenarios where at least one letter is placed incorrectly is $6-1=5$.