Six cards and six envelopes are numbered $1$, $2$, $3$, $4$, $5$, $6$ and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered $1$ is always placed in envelope numbered $2$. Then, what is the number of ways this can be done?
Since card one is already fixed, I tried directly applying the Derangement formula for $5$ things.
But it didn't work. I guess it's not so simple since the envelope no. $2$ is already occupied.
I just need a hint on how to proceed.
Hint: Show that exactly $1/5$ of all derangements have "card 1" in "envelope 2".