Letters in Mailboxes so that none are in the right one In how many ways can 5 letters be put in 5 mailboxes such that none are placed in the right one ? I creatively thought labeling the letters & mailboxes 1-5 ,  it would be saying letter 1 can be placed in any of the other four . So a total of 4^5 ways .this was not one of the answers . Then i thought hmm lets write as an example 13254 as a sequence above 12345 ..this sequence is a ' throw-out ' case because the 1 cant go with the 1. This would generate _ _ a two digit number ..one for the letter and one for the mailbox .as an example 12 is legit . ( letter 1 in mailbox 2 ) while the pairs 11,22, ect are not .
This would give 5 possabilities for the first number and 5 for the second , or 5x5 =25. But then we must subtract out the posabilities of the 11, 22, 33, ect 
This gives 25- 5 =20 but that is STILL not one of the answers 

These are known as derangements.
Look here:
https://en.wikipedia.org/wiki/Derangement
