4 different letters are dropped on the floor and then inserted into four differently addressed envelopes. Find the probability that exactly 2 letters are inserted into the proper envelope.

Answer 1

It doesn't take long to list these cases, using uppercase letters to show correct placement and lowercase letters to show incorrect placement:

ABdc
AdCb
AcbD
dBCa
cBaD
baCD

We see there are 6 ways for this event to happen, or 4c2, out of 4! total possible ways of placing the letters in envelopes.

4c2/4! = ______