Asked by James

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.

Answers

Answered by plumpycat
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! = ______


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