In how many ways we can put $5$ writings into $5$ corresponding envelopes so that no writing go to the corresponding envelope$?$

Q. In how many ways $5$ letters go into $5$ envelopes such that exactly $1$ letter goes in to corresponding envelope?

Q. A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that all of them are in wrong envelope.

Q. A person writes letters to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wring envelope.

Q. A person writes a letter to six friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong places?

Q. In how many ways 6 letters can be put in 6 addressed envelopes so that only 5 of them will go in the correct envelopes.